Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms
Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Li, Xiaoyan [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2023 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales - Heidelberg [u.a.] : Springer, 2001, 117(2023), 3 vom: 27. Apr. |
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| Übergeordnetes Werk: |
volume:117 ; year:2023 ; number:3 ; day:27 ; month:04 |
| Links: |
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| DOI / URN: |
10.1007/s13398-023-01439-1 |
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| Katalog-ID: |
SPR05022011X |
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| 245 | 1 | 0 | |a Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms |
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| 520 | |a Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. | ||
| 650 | 4 | |a Orlicz sequence space |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a -Amemiya norm |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Smooth point |7 (dpeaa)DE-He213 | |
| 650 | 4 | |a Very (strongly) smooth point |7 (dpeaa)DE-He213 | |
| 700 | 1 | |a Cui, Yunan |0 (orcid)0000-0001-6756-2233 |4 aut | |
| 700 | 1 | |a Wisła, Marek |4 aut | |
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| 856 | 4 | 0 | |u https://dx.doi.org/10.1007/s13398-023-01439-1 |z lizenzpflichtig |3 Volltext |
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10.1007/s13398-023-01439-1 doi (DE-627)SPR05022011X (SPR)s13398-023-01439-1-e DE-627 ger DE-627 rakwb eng Li, Xiaoyan verfasserin aut Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. Orlicz sequence space (dpeaa)DE-He213 -Amemiya norm (dpeaa)DE-He213 Smooth point (dpeaa)DE-He213 Very (strongly) smooth point (dpeaa)DE-He213 Cui, Yunan (orcid)0000-0001-6756-2233 aut Wisła, Marek aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 117(2023), 3 vom: 27. Apr. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:117 year:2023 number:3 day:27 month:04 https://dx.doi.org/10.1007/s13398-023-01439-1 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_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 117 2023 3 27 04 |
| spelling |
10.1007/s13398-023-01439-1 doi (DE-627)SPR05022011X (SPR)s13398-023-01439-1-e DE-627 ger DE-627 rakwb eng Li, Xiaoyan verfasserin aut Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. Orlicz sequence space (dpeaa)DE-He213 -Amemiya norm (dpeaa)DE-He213 Smooth point (dpeaa)DE-He213 Very (strongly) smooth point (dpeaa)DE-He213 Cui, Yunan (orcid)0000-0001-6756-2233 aut Wisła, Marek aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 117(2023), 3 vom: 27. Apr. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:117 year:2023 number:3 day:27 month:04 https://dx.doi.org/10.1007/s13398-023-01439-1 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_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 117 2023 3 27 04 |
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10.1007/s13398-023-01439-1 doi (DE-627)SPR05022011X (SPR)s13398-023-01439-1-e DE-627 ger DE-627 rakwb eng Li, Xiaoyan verfasserin aut Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. Orlicz sequence space (dpeaa)DE-He213 -Amemiya norm (dpeaa)DE-He213 Smooth point (dpeaa)DE-He213 Very (strongly) smooth point (dpeaa)DE-He213 Cui, Yunan (orcid)0000-0001-6756-2233 aut Wisła, Marek aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 117(2023), 3 vom: 27. Apr. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:117 year:2023 number:3 day:27 month:04 https://dx.doi.org/10.1007/s13398-023-01439-1 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_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 117 2023 3 27 04 |
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10.1007/s13398-023-01439-1 doi (DE-627)SPR05022011X (SPR)s13398-023-01439-1-e DE-627 ger DE-627 rakwb eng Li, Xiaoyan verfasserin aut Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. Orlicz sequence space (dpeaa)DE-He213 -Amemiya norm (dpeaa)DE-He213 Smooth point (dpeaa)DE-He213 Very (strongly) smooth point (dpeaa)DE-He213 Cui, Yunan (orcid)0000-0001-6756-2233 aut Wisła, Marek aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 117(2023), 3 vom: 27. Apr. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:117 year:2023 number:3 day:27 month:04 https://dx.doi.org/10.1007/s13398-023-01439-1 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_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 117 2023 3 27 04 |
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10.1007/s13398-023-01439-1 doi (DE-627)SPR05022011X (SPR)s13398-023-01439-1-e DE-627 ger DE-627 rakwb eng Li, Xiaoyan verfasserin aut Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms 2023 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. Orlicz sequence space (dpeaa)DE-He213 -Amemiya norm (dpeaa)DE-He213 Smooth point (dpeaa)DE-He213 Very (strongly) smooth point (dpeaa)DE-He213 Cui, Yunan (orcid)0000-0001-6756-2233 aut Wisła, Marek aut Enthalten in Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales Heidelberg [u.a.] : Springer, 2001 117(2023), 3 vom: 27. Apr. (DE-627)495744433 (DE-600)2198482-7 1579-1505 nnns volume:117 year:2023 number:3 day:27 month:04 https://dx.doi.org/10.1007/s13398-023-01439-1 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_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 117 2023 3 27 04 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. 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Li, Xiaoyan |
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Li, Xiaoyan misc Orlicz sequence space misc -Amemiya norm misc Smooth point misc Very (strongly) smooth point Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms |
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smoothness, very (strongly) smoothness of orlicz sequence spaces equipped with p-amemiya norms |
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Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms |
| abstract |
Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract In this paper, a new convex modular %$\rho ^{*}(f)%$ is introduced. Using the concept of %$\rho ^{*}(f)%$, we will investigate %$\Vert f\Vert _{\varPsi ,q}^{*}%$ in Orlicz sequence spaces defined by the formula %$ \Vert f\Vert _{\varPsi ,q}^{*}=\inf _{k>0}\frac{1}{k}s_{q}(\rho ^{*}(kf))%$, which is the norm formula in Orlicz sequence dual spaces equipped with p-Amemiya norms. By presenting the explicit form of supporting functional, we get sufficient and necessary conditions for smooth points, very (strongly) smooth points. As a result, criteria for smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya %$(1\le p <\infty )%$ norms are also obtained. The obtained results unify, complete and extend as well the results presented by a number of papers devoted to studying the geometry of Orlicz sequence spaces endowed with the Orlicz norm. © The Author(s) under exclusive licence to The Royal Academy of Sciences, Madrid 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Smoothness, very (strongly) smoothness of Orlicz sequence spaces equipped with p-Amemiya norms |
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https://dx.doi.org/10.1007/s13398-023-01439-1 |
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Cui, Yunan Wisła, Marek |
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Cui, Yunan Wisła, Marek |
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10.1007/s13398-023-01439-1 |
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2024-07-03T14:08:49.071Z |
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|
| score |
7.3998604 |