The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces

Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E...
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Autor*in:	Zhukovskiy, E. S. [verfasserIn] Panasenko, E. A. [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2024

Schlagwörter:	operator inclusion existence and estimates of solutions integral inclusion vector metric space

Anmerkung:	© Pleiades Publishing, Ltd. 2024

Übergeordnetes Werk:	Enthalten in: Proceedings of the Steklov Institute of Mathematics - Pleiades Publishing, 2006, 325(2024), Suppl 1 vom: Aug., Seite S239-S254
Übergeordnetes Werk:	volume:325 ; year:2024 ; number:Suppl 1 ; month:08 ; pages:S239-S254

Links:	Volltext

DOI / URN:	10.1134/S0081543824030180

Katalog-ID:	SPR057030537

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520			\|a Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion.
650		4	\|a operator inclusion \|7 (dpeaa)DE-He213
650		4	\|a existence and estimates of solutions \|7 (dpeaa)DE-He213
650		4	\|a integral inclusion \|7 (dpeaa)DE-He213
650		4	\|a vector metric space \|7 (dpeaa)DE-He213
700	1		\|a Panasenko, E. A. \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Proceedings of the Steklov Institute of Mathematics \|d Pleiades Publishing, 2006 \|g 325(2024), Suppl 1 vom: Aug., Seite S239-S254 \|w (DE-627)515978507 \|w (DE-600)2244577-8 \|x 1531-8605 \|7 nnns
773	1	8	\|g volume:325 \|g year:2024 \|g number:Suppl 1 \|g month:08 \|g pages:S239-S254
856	4	0	\|u https://dx.doi.org/10.1134/S0081543824030180 \|m X:SPRINGER \|x Resolving-System \|z lizenzpflichtig \|3 Volltext
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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_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
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912			\|a GBV_ILN_602
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allfields	10.1134/S0081543824030180 doi (DE-627)SPR057030537 (SPR)S0081543824030180-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Zhukovskiy, E. S. verfasserin aut The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2024 Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213 Panasenko, E. A. verfasserin aut Enthalten in Proceedings of the Steklov Institute of Mathematics Pleiades Publishing, 2006 325(2024), Suppl 1 vom: Aug., Seite S239-S254 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254 https://dx.doi.org/10.1134/S0081543824030180 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2056 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_2122 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 325 2024 Suppl 1 08 S239-S254
spelling	10.1134/S0081543824030180 doi (DE-627)SPR057030537 (SPR)S0081543824030180-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Zhukovskiy, E. S. verfasserin aut The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2024 Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213 Panasenko, E. A. verfasserin aut Enthalten in Proceedings of the Steklov Institute of Mathematics Pleiades Publishing, 2006 325(2024), Suppl 1 vom: Aug., Seite S239-S254 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254 https://dx.doi.org/10.1134/S0081543824030180 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2056 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_2122 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 325 2024 Suppl 1 08 S239-S254
allfields_unstemmed	10.1134/S0081543824030180 doi (DE-627)SPR057030537 (SPR)S0081543824030180-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Zhukovskiy, E. S. verfasserin aut The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2024 Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213 Panasenko, E. A. verfasserin aut Enthalten in Proceedings of the Steklov Institute of Mathematics Pleiades Publishing, 2006 325(2024), Suppl 1 vom: Aug., Seite S239-S254 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254 https://dx.doi.org/10.1134/S0081543824030180 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2056 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_2122 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 325 2024 Suppl 1 08 S239-S254
allfieldsGer	10.1134/S0081543824030180 doi (DE-627)SPR057030537 (SPR)S0081543824030180-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Zhukovskiy, E. S. verfasserin aut The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2024 Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213 Panasenko, E. A. verfasserin aut Enthalten in Proceedings of the Steklov Institute of Mathematics Pleiades Publishing, 2006 325(2024), Suppl 1 vom: Aug., Seite S239-S254 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254 https://dx.doi.org/10.1134/S0081543824030180 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2056 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_2122 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 325 2024 Suppl 1 08 S239-S254
allfieldsSound	10.1134/S0081543824030180 doi (DE-627)SPR057030537 (SPR)S0081543824030180-e DE-627 ger DE-627 rakwb eng 510 VZ 510 VZ 31.00 bkl Zhukovskiy, E. S. verfasserin aut The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Pleiades Publishing, Ltd. 2024 Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213 Panasenko, E. A. verfasserin aut Enthalten in Proceedings of the Steklov Institute of Mathematics Pleiades Publishing, 2006 325(2024), Suppl 1 vom: Aug., Seite S239-S254 (DE-627)515978507 (DE-600)2244577-8 1531-8605 nnns volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254 https://dx.doi.org/10.1134/S0081543824030180 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER SSG-OPC-MAT 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_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 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_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_2056 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_2122 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_4126 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_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 31.00 VZ AR 325 2024 Suppl 1 08 S239-S254
language	English
source	Enthalten in Proceedings of the Steklov Institute of Mathematics 325(2024), Suppl 1 vom: Aug., Seite S239-S254 volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254
sourceStr	Enthalten in Proceedings of the Steklov Institute of Mathematics 325(2024), Suppl 1 vom: Aug., Seite S239-S254 volume:325 year:2024 number:Suppl 1 month:08 pages:S239-S254
format_phy_str_mv	Article
institution	findex.gbv.de
topic_facet	operator inclusion existence and estimates of solutions integral inclusion vector metric space
dewey-raw	510
isfreeaccess_bool	false
container_title	Proceedings of the Steklov Institute of Mathematics
authorswithroles_txt_mv	Zhukovskiy, E. S. @@aut@@ Panasenko, E. A. @@aut@@
publishDateDaySort_date	2024-08-01T00:00:00Z
hierarchy_top_id	515978507
dewey-sort	3510
id	SPR057030537
language_de	englisch
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The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. 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author	Zhukovskiy, E. S.
spellingShingle	Zhukovskiy, E. S. ddc 510 bkl 31.00 misc operator inclusion misc existence and estimates of solutions misc integral inclusion misc vector metric space The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces
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topic_title	510 VZ 31.00 bkl The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces operator inclusion (dpeaa)DE-He213 existence and estimates of solutions (dpeaa)DE-He213 integral inclusion (dpeaa)DE-He213 vector metric space (dpeaa)DE-He213
topic	ddc 510 bkl 31.00 misc operator inclusion misc existence and estimates of solutions misc integral inclusion misc vector metric space
topic_unstemmed	ddc 510 bkl 31.00 misc operator inclusion misc existence and estimates of solutions misc integral inclusion misc vector metric space
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title	The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces
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title_full	The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces
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author_browse	Zhukovskiy, E. S. Panasenko, E. A.
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title_sort	the method of comparison with a model equation in the study of inclusions in vector metric spaces
title_auth	The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces
abstract	Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. © Pleiades Publishing, Ltd. 2024
abstractGer	Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. © Pleiades Publishing, Ltd. 2024
abstract_unstemmed	Abstract For a given multivalued mapping $$F:X\rightrightarrows Y$$ and a given element $$\tilde{y}\in Y$$, the existence of a solution $$x\in X$$ to the inclusion $$F(x)\ni\tilde{y}$$ and its estimates are studied. The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. Further, conditions on the connection between $$f(0)$$ and $$F(x_{0})$$ and between the increments of $$f(t)$$ for $$t\in[0,t^{}]$$ and the increments of $$F(x)$$ for all $$x$$ in the ball of radius $$t^{*}$$ centered at $$x_{0}$$ for some $$x_{0}$$ are formulated, and it is shown that the inclusion has a solution in the ball under these conditions. The results on the operator inclusion obtained in the paper are applied to studying an integral inclusion. © Pleiades Publishing, Ltd. 2024
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container_issue	Suppl 1
title_short	The Method of Comparison with a Model Equation in the Study of Inclusions in Vector Metric Spaces
url	https://dx.doi.org/10.1134/S0081543824030180
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author2	Panasenko, E. A.
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The sets $$X$$ and $$Y$$ are endowed with vector-valued metrics $$\mathcal{P}_{X}^{E_{+}}$$ and $$\mathcal{P}_{Y}^{M_{+}}$$, whose values belong to cones $$E_{+}$$ and $$M_{+}$$ of a Banach space $$E$$ and a linear topological space $$M$$, respectively. The inclusion is compared with a “model” equation $$f(t)=0$$, where $$f:E_{+}\to M$$. It is assumed that $$f$$ can be written as $$f(t)\equiv g(t,t)$$, where the mapping $$g:{E}_{+}\times{E}_{+}\to M$$ orderly covers the set $$\{0\}\subset M$$ with respect to the first argument and is antitone with respect to the second argument and $$-g(0,0)\in M_{+}$$. It is shown that, in this case, the equation $$f(t)=0$$ has a solution $$t^{}\in E_{+}$$. 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