On New Moduli Related to the Generalization of the Parallelogram Law
Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach s...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Liu, Qi [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2021 |
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| Schlagwörter: |
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| Anmerkung: |
© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 |
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| Übergeordnetes Werk: |
Enthalten in: Bulletin of the Malaysian Mathematical Sciences Society - [Singapore] : Springer Singapore, 2000, 45(2021), 1 vom: 21. Sept., Seite 307-321 |
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| Übergeordnetes Werk: |
volume:45 ; year:2021 ; number:1 ; day:21 ; month:09 ; pages:307-321 |
| Links: |
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| DOI / URN: |
10.1007/s40840-021-01196-7 |
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| Katalog-ID: |
SPR045793611 |
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| 100 | 1 | |a Liu, Qi |e verfasserin |4 aut | |
| 245 | 1 | 0 | |a On New Moduli Related to the Generalization of the Parallelogram Law |
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| 520 | |a Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. | ||
| 650 | 4 | |a Banach spaces |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Geometric constants |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Normal structure |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Euler–Lagrange identity |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Zhou, Chuanjiang |4 aut | |
| 700 | 1 | |a Sarfraz, Muhammad |4 aut | |
| 700 | 1 | |a Li, Yongjin |4 aut | |
| 773 | 0 | 8 | |i Enthalten in |t Bulletin of the Malaysian Mathematical Sciences Society |d [Singapore] : Springer Singapore, 2000 |g 45(2021), 1 vom: 21. Sept., Seite 307-321 |w (DE-627)843984465 |w (DE-600)2842782-8 |x 2180-4206 |7 nnns |
| 773 | 1 | 8 | |g volume:45 |g year:2021 |g number:1 |g day:21 |g month:09 |g pages:307-321 |
| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s40840-021-01196-7 |z lizenzpflichtig |3 Volltext |
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10.1007/s40840-021-01196-7 doi (DE-627)SPR045793611 (SPR)s40840-021-01196-7-e DE-627 ger DE-627 rakwb eng Liu, Qi verfasserin aut On New Moduli Related to the Generalization of the Parallelogram Law 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 Zhou, Chuanjiang aut Sarfraz, Muhammad aut Li, Yongjin aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 45(2021), 1 vom: 21. Sept., Seite 307-321 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:45 year:2021 number:1 day:21 month:09 pages:307-321 https://dx.doi.org/10.1007/s40840-021-01196-7 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_152 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_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_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 AR 45 2021 1 21 09 307-321 |
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10.1007/s40840-021-01196-7 doi (DE-627)SPR045793611 (SPR)s40840-021-01196-7-e DE-627 ger DE-627 rakwb eng Liu, Qi verfasserin aut On New Moduli Related to the Generalization of the Parallelogram Law 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 Zhou, Chuanjiang aut Sarfraz, Muhammad aut Li, Yongjin aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 45(2021), 1 vom: 21. Sept., Seite 307-321 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:45 year:2021 number:1 day:21 month:09 pages:307-321 https://dx.doi.org/10.1007/s40840-021-01196-7 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_152 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_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_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 AR 45 2021 1 21 09 307-321 |
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10.1007/s40840-021-01196-7 doi (DE-627)SPR045793611 (SPR)s40840-021-01196-7-e DE-627 ger DE-627 rakwb eng Liu, Qi verfasserin aut On New Moduli Related to the Generalization of the Parallelogram Law 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 Zhou, Chuanjiang aut Sarfraz, Muhammad aut Li, Yongjin aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 45(2021), 1 vom: 21. Sept., Seite 307-321 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:45 year:2021 number:1 day:21 month:09 pages:307-321 https://dx.doi.org/10.1007/s40840-021-01196-7 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_152 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_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_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 AR 45 2021 1 21 09 307-321 |
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10.1007/s40840-021-01196-7 doi (DE-627)SPR045793611 (SPR)s40840-021-01196-7-e DE-627 ger DE-627 rakwb eng Liu, Qi verfasserin aut On New Moduli Related to the Generalization of the Parallelogram Law 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 Zhou, Chuanjiang aut Sarfraz, Muhammad aut Li, Yongjin aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 45(2021), 1 vom: 21. Sept., Seite 307-321 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:45 year:2021 number:1 day:21 month:09 pages:307-321 https://dx.doi.org/10.1007/s40840-021-01196-7 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_152 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_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_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 AR 45 2021 1 21 09 307-321 |
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10.1007/s40840-021-01196-7 doi (DE-627)SPR045793611 (SPR)s40840-021-01196-7-e DE-627 ger DE-627 rakwb eng Liu, Qi verfasserin aut On New Moduli Related to the Generalization of the Parallelogram Law 2021 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 Zhou, Chuanjiang aut Sarfraz, Muhammad aut Li, Yongjin aut Enthalten in Bulletin of the Malaysian Mathematical Sciences Society [Singapore] : Springer Singapore, 2000 45(2021), 1 vom: 21. Sept., Seite 307-321 (DE-627)843984465 (DE-600)2842782-8 2180-4206 nnns volume:45 year:2021 number:1 day:21 month:09 pages:307-321 https://dx.doi.org/10.1007/s40840-021-01196-7 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_152 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_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_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 AR 45 2021 1 21 09 307-321 |
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Enthalten in Bulletin of the Malaysian Mathematical Sciences Society 45(2021), 1 vom: 21. Sept., Seite 307-321 volume:45 year:2021 number:1 day:21 month:09 pages:307-321 |
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Liu, Qi |
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Liu, Qi misc Banach spaces misc Geometric constants misc Normal structure misc Euler–Lagrange identity On New Moduli Related to the Generalization of the Parallelogram Law |
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On New Moduli Related to the Generalization of the Parallelogram Law Banach spaces (dpeaa)DE-He213 Geometric constants (dpeaa)DE-He213 Normal structure (dpeaa)DE-He213 Euler–Lagrange identity (dpeaa)DE-He213 |
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On New Moduli Related to the Generalization of the Parallelogram Law |
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Liu, Qi Zhou, Chuanjiang Sarfraz, Muhammad Li, Yongjin |
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10.1007/s40840-021-01196-7 |
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on new moduli related to the generalization of the parallelogram law |
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On New Moduli Related to the Generalization of the Parallelogram Law |
| abstract |
Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 |
| abstractGer |
Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 |
| abstract_unstemmed |
Abstract We shall introduce a new geometric constant %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ based on a generalization of the parallelogram law, which was proposed by Moslehian and Rassias. We first discuss some basic properties of this new coefficient. Next, it is shown that, for a Banach space, %$L^{\prime }_{\mathrm {YJ}}(\lambda ,\mu ,X)%$ becomes 1 if and only if the norm is induced by an inner product. Moreover, some sufficient conditions which imply normal structure are presented. Finally, we describe some relations between the well-known geometric constants and %$L^{\prime }_{\mathrm {YJ}}(\lambda , \mu ,X)%$ through some inequalities. © Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2021 |
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On New Moduli Related to the Generalization of the Parallelogram Law |
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Zhou, Chuanjiang Sarfraz, Muhammad Li, Yongjin |
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| doi_str |
10.1007/s40840-021-01196-7 |
| up_date |
2024-07-03T18:19:56.788Z |
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