Convolution and Convex Combination of Harmonic Mappings

Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in th...
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Autor*in:	Beig, Subzar [verfasserIn] Ravichandran, V.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2019

Schlagwörter:	Harmonic mappings Directional convexity Convolution Convex combination Dilatation Univalency

Anmerkung:	© Iranian Mathematical Society 2019

Übergeordnetes Werk:	Enthalten in: Bulletin of the Iranian Mathematical Society - Singapore : Springer Singapore, 2001, 45(2019), 5 vom: 08. März, Seite 1467-1486
Übergeordnetes Werk:	volume:45 ; year:2019 ; number:5 ; day:08 ; month:03 ; pages:1467-1486

Links:	Volltext

DOI / URN:	10.1007/s41980-019-00209-3

Katalog-ID:	SPR038362848

Internformat


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245	1	0	\|a Convolution and Convex Combination of Harmonic Mappings
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520			\|a Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction.
650		4	\|a Harmonic mappings \|7 (dpeaa)DE-He213
650		4	\|a Directional convexity \|7 (dpeaa)DE-He213
650		4	\|a Convolution \|7 (dpeaa)DE-He213
650		4	\|a Convex combination \|7 (dpeaa)DE-He213
650		4	\|a Dilatation \|7 (dpeaa)DE-He213
650		4	\|a Univalency \|7 (dpeaa)DE-He213
700	1		\|a Ravichandran, V. \|0 (orcid)0000-0002-3632-7529 \|4 aut
773	0	8	\|i Enthalten in \|t Bulletin of the Iranian Mathematical Society \|d Singapore : Springer Singapore, 2001 \|g 45(2019), 5 vom: 08. März, Seite 1467-1486 \|w (DE-627)573093903 \|w (DE-600)2440200-X \|x 1735-8515 \|7 nnns
773	1	8	\|g volume:45 \|g year:2019 \|g number:5 \|g day:08 \|g month:03 \|g pages:1467-1486
856	4	0	\|u https://dx.doi.org/10.1007/s41980-019-00209-3 \|z lizenzpflichtig \|3 Volltext
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912			\|a GBV_ILN_22
912			\|a GBV_ILN_23
912			\|a GBV_ILN_24
912			\|a GBV_ILN_31
912			\|a GBV_ILN_32
912			\|a GBV_ILN_39
912			\|a GBV_ILN_40
912			\|a GBV_ILN_60
912			\|a GBV_ILN_62
912			\|a GBV_ILN_63
912			\|a GBV_ILN_65
912			\|a GBV_ILN_69
912			\|a GBV_ILN_70
912			\|a GBV_ILN_73
912			\|a GBV_ILN_74
912			\|a GBV_ILN_90
912			\|a GBV_ILN_95
912			\|a GBV_ILN_100
912			\|a GBV_ILN_105
912			\|a GBV_ILN_110
912			\|a GBV_ILN_120
912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_266
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2008
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
912			\|a GBV_ILN_2148
912			\|a GBV_ILN_2152
912			\|a GBV_ILN_2153
912			\|a GBV_ILN_2188
912			\|a GBV_ILN_2190
912			\|a GBV_ILN_2232
912			\|a GBV_ILN_2336
912			\|a GBV_ILN_2446
912			\|a GBV_ILN_2470
912			\|a GBV_ILN_2472
912			\|a GBV_ILN_2507
912			\|a GBV_ILN_2522
912			\|a GBV_ILN_2548
912			\|a GBV_ILN_4035
912			\|a GBV_ILN_4037
912			\|a GBV_ILN_4046
912			\|a GBV_ILN_4112
912			\|a GBV_ILN_4125
912			\|a GBV_ILN_4242
912			\|a GBV_ILN_4246
912			\|a GBV_ILN_4249
912			\|a GBV_ILN_4251
912			\|a GBV_ILN_4305
912			\|a GBV_ILN_4306
912			\|a GBV_ILN_4307
912			\|a GBV_ILN_4313
912			\|a GBV_ILN_4322
912			\|a GBV_ILN_4323
912			\|a GBV_ILN_4324
912			\|a GBV_ILN_4325
912			\|a GBV_ILN_4326
912			\|a GBV_ILN_4333
912			\|a GBV_ILN_4334
912			\|a GBV_ILN_4335
912			\|a GBV_ILN_4336
912			\|a GBV_ILN_4338
912			\|a GBV_ILN_4393
912			\|a GBV_ILN_4700
951			\|a AR
952			\|d 45 \|j 2019 \|e 5 \|b 08 \|c 03 \|h 1467-1486

Indexfelder

author_variant	s b sb v r vr
matchkey_str	article:17358515:2019----::ovltoadovxobntoohr
hierarchy_sort_str	2019
publishDate	2019
allfields	10.1007/s41980-019-00209-3 doi (DE-627)SPR038362848 (SPR)s41980-019-00209-3-e DE-627 ger DE-627 rakwb eng Beig, Subzar verfasserin aut Convolution and Convex Combination of Harmonic Mappings 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213 Ravichandran, V. (orcid)0000-0002-3632-7529 aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 5 vom: 08. März, Seite 1467-1486 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486 https://dx.doi.org/10.1007/s41980-019-00209-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 5 08 03 1467-1486
spelling	10.1007/s41980-019-00209-3 doi (DE-627)SPR038362848 (SPR)s41980-019-00209-3-e DE-627 ger DE-627 rakwb eng Beig, Subzar verfasserin aut Convolution and Convex Combination of Harmonic Mappings 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213 Ravichandran, V. (orcid)0000-0002-3632-7529 aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 5 vom: 08. März, Seite 1467-1486 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486 https://dx.doi.org/10.1007/s41980-019-00209-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 5 08 03 1467-1486
allfields_unstemmed	10.1007/s41980-019-00209-3 doi (DE-627)SPR038362848 (SPR)s41980-019-00209-3-e DE-627 ger DE-627 rakwb eng Beig, Subzar verfasserin aut Convolution and Convex Combination of Harmonic Mappings 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213 Ravichandran, V. (orcid)0000-0002-3632-7529 aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 5 vom: 08. März, Seite 1467-1486 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486 https://dx.doi.org/10.1007/s41980-019-00209-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 5 08 03 1467-1486
allfieldsGer	10.1007/s41980-019-00209-3 doi (DE-627)SPR038362848 (SPR)s41980-019-00209-3-e DE-627 ger DE-627 rakwb eng Beig, Subzar verfasserin aut Convolution and Convex Combination of Harmonic Mappings 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213 Ravichandran, V. (orcid)0000-0002-3632-7529 aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 5 vom: 08. März, Seite 1467-1486 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486 https://dx.doi.org/10.1007/s41980-019-00209-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 5 08 03 1467-1486
allfieldsSound	10.1007/s41980-019-00209-3 doi (DE-627)SPR038362848 (SPR)s41980-019-00209-3-e DE-627 ger DE-627 rakwb eng Beig, Subzar verfasserin aut Convolution and Convex Combination of Harmonic Mappings 2019 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Iranian Mathematical Society 2019 Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213 Ravichandran, V. (orcid)0000-0002-3632-7529 aut Enthalten in Bulletin of the Iranian Mathematical Society Singapore : Springer Singapore, 2001 45(2019), 5 vom: 08. März, Seite 1467-1486 (DE-627)573093903 (DE-600)2440200-X 1735-8515 nnns volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486 https://dx.doi.org/10.1007/s41980-019-00209-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_266 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 45 2019 5 08 03 1467-1486
language	English
source	Enthalten in Bulletin of the Iranian Mathematical Society 45(2019), 5 vom: 08. März, Seite 1467-1486 volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486
sourceStr	Enthalten in Bulletin of the Iranian Mathematical Society 45(2019), 5 vom: 08. März, Seite 1467-1486 volume:45 year:2019 number:5 day:08 month:03 pages:1467-1486
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	Harmonic mappings Directional convexity Convolution Convex combination Dilatation Univalency
isfreeaccess_bool	false
container_title	Bulletin of the Iranian Mathematical Society
authorswithroles_txt_mv	Beig, Subzar @@aut@@ Ravichandran, V. @@aut@@
publishDateDaySort_date	2019-03-08T00:00:00Z
hierarchy_top_id	573093903
id	SPR038362848
language_de	englisch
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In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic mappings</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Directional convexity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convolution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex combination</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dilatation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Univalency</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ravichandran, V.</subfield><subfield code="0">(orcid)0000-0002-3632-7529</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of the Iranian Mathematical Society</subfield><subfield code="d">Singapore : Springer Singapore, 2001</subfield><subfield code="g">45(2019), 5 vom: 08. 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author	Beig, Subzar
spellingShingle	Beig, Subzar misc Harmonic mappings misc Directional convexity misc Convolution misc Convex combination misc Dilatation misc Univalency Convolution and Convex Combination of Harmonic Mappings
authorStr	Beig, Subzar
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topic_title	Convolution and Convex Combination of Harmonic Mappings Harmonic mappings (dpeaa)DE-He213 Directional convexity (dpeaa)DE-He213 Convolution (dpeaa)DE-He213 Convex combination (dpeaa)DE-He213 Dilatation (dpeaa)DE-He213 Univalency (dpeaa)DE-He213
topic	misc Harmonic mappings misc Directional convexity misc Convolution misc Convex combination misc Dilatation misc Univalency
topic_unstemmed	misc Harmonic mappings misc Directional convexity misc Convolution misc Convex combination misc Dilatation misc Univalency
topic_browse	misc Harmonic mappings misc Directional convexity misc Convolution misc Convex combination misc Dilatation misc Univalency
format_facet	Elektronische Aufsätze Aufsätze Elektronische Ressource
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title	Convolution and Convex Combination of Harmonic Mappings
ctrlnum	(DE-627)SPR038362848 (SPR)s41980-019-00209-3-e
title_full	Convolution and Convex Combination of Harmonic Mappings
author_sort	Beig, Subzar
journal	Bulletin of the Iranian Mathematical Society
journalStr	Bulletin of the Iranian Mathematical Society
lang_code	eng
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container_start_page	1467
author_browse	Beig, Subzar Ravichandran, V.
container_volume	45
format_se	Elektronische Aufsätze
author-letter	Beig, Subzar
doi_str_mv	10.1007/s41980-019-00209-3
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title_sort	convolution and convex combination of harmonic mappings
title_auth	Convolution and Convex Combination of Harmonic Mappings
abstract	Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. © Iranian Mathematical Society 2019
abstractGer	Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. © Iranian Mathematical Society 2019
abstract_unstemmed	Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction. © Iranian Mathematical Society 2019
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container_issue	5
title_short	Convolution and Convex Combination of Harmonic Mappings
url	https://dx.doi.org/10.1007/s41980-019-00209-3
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author2	Ravichandran, V.
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doi_str	10.1007/s41980-019-00209-3
up_date	2024-07-03T17:37:48.310Z
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fullrecord_marcxml	<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">SPR038362848</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230328202239.0</controlfield><controlfield tag="007">cr uuu---uuuuu</controlfield><controlfield tag="008">201007s2019 xx \|\|\|\|\|o 00\| \|\|eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s41980-019-00209-3</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)SPR038362848</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(SPR)s41980-019-00209-3-e</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Beig, Subzar</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Convolution and Convex Combination of Harmonic Mappings</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2019</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">Computermedien</subfield><subfield code="b">c</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Online-Ressource</subfield><subfield code="b">cr</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Iranian Mathematical Society 2019</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract For each %$a\in [0,1)%$, the convolution of the right half-plane harmonic mapping having dilatation %$(a-z)/(1-az)%$ with the right half-plane harmonic mapping having dilatation %$\left( a-z^2\right) /\left( 1-az^2\right) %$ or %$-(a-z)^2/(1-az)^2%$ is shown to be univalent and convex in the real direction. In addition, sufficient conditions are found for the convex combination of the harmonic mappings %$f_i=h_i+\overline{g_i}%$, %$i=1,2%$ satisfying hi(z)+gi(z)=∫0z(1-w2n)(1+w2n+αiw2n-1)1-w2(1+w2n+1)dw,-1≤αi≤1,n≥1,%$\begin{aligned} h_i(z)+g_i(z)=\int _0^z\frac{(1-w^{2^{n}})(1+w^{2^n}+\alpha _i w^{2^{n-1}})}{\left( 1-w^2\right) (1+w^{2^{n+1}})}\mathrm{{d}}w,\quad -1\le \alpha _i\le 1, \quad n\ge 1, \end{aligned}%$to be univalent and convex in the real direction.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Harmonic mappings</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Directional convexity</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convolution</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Convex combination</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Dilatation</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Univalency</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Ravichandran, V.</subfield><subfield code="0">(orcid)0000-0002-3632-7529</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Bulletin of the Iranian Mathematical Society</subfield><subfield code="d">Singapore : Springer Singapore, 2001</subfield><subfield code="g">45(2019), 5 vom: 08. 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