On uniform convexity of linear metric spaces
UDC 517 The notion of uniform convexity was introduced and discussed in normed linear spaces by Clarkson [Trans. Amer. Math. Soc., 40, 396–414 (1936)]. Later, this idea attracted attention of other researchers who studied these spaces in depth and also introduced and analyzed in detail numerous othe...
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Institute of Mathematics, NAS of Ukraine
2025
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512932367958016 |
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| author | Grover, Harpreet K. Garg, Shelly Narang, T. D. Grover, Harpreet K. Garg, Shelly Narang, T. D. |
| author_facet | Grover, Harpreet K. Garg, Shelly Narang, T. D. Grover, Harpreet K. Garg, Shelly Narang, T. D. |
| author_sort | Grover, Harpreet K. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-11-05T09:34:36Z |
| description | UDC 517
The notion of uniform convexity was introduced and discussed in normed linear spaces by Clarkson [Trans. Amer. Math. Soc., 40, 396–414 (1936)]. Later, this idea attracted attention of other researchers who studied these spaces in depth and also introduced and analyzed in detail numerous other weaker forms of uniform convexity. Further, the idea of uniform convexity and its weaker forms was also extended to linear metric spaces. Over the years, the researchers investigated and analyzed the properties of linear metric spaces equipped either with uniform convexity or with its weaker forms, and studied their relationships, inheritance of these properties by quotient spaces, and the applications of these properties to many other domains of mathematics. In this article, we survey the available literature on these topics in linear metric spaces. |
| doi_str_mv | 10.3842/umzh.v77i2.8145 |
| first_indexed | 2026-03-24T03:36:38Z |
| format | Article |
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| id | umjimathkievua-article-8145 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-03-24T03:36:38Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
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| spelling | umjimathkievua-article-81452025-11-05T09:34:36Z On uniform convexity of linear metric spaces On uniform convexity of linear metric spaces Grover, Harpreet K. Garg, Shelly Narang, T. D. Grover, Harpreet K. Garg, Shelly Narang, T. D. Linear metric space, strictly convex, uniformly convex, U.C.I/II/III/IV/V. UDC 517 The notion of uniform convexity was introduced and discussed in normed linear spaces by Clarkson [Trans. Amer. Math. Soc., 40, 396–414 (1936)]. Later, this idea attracted attention of other researchers who studied these spaces in depth and also introduced and analyzed in detail numerous other weaker forms of uniform convexity. Further, the idea of uniform convexity and its weaker forms was also extended to linear metric spaces. Over the years, the researchers investigated and analyzed the properties of linear metric spaces equipped either with uniform convexity or with its weaker forms, and studied their relationships, inheritance of these properties by quotient spaces, and the applications of these properties to many other domains of mathematics. In this article, we survey the available literature on these topics in linear metric spaces. УДК 517 Про рівномірну опуклість лінійних метричних просторів Поняття рівномірної опуклості було введено та обговорено в нормованих лінійних просторах Кларксоном [Trans. Amer. Math. Soc., 40, 396–414 (1936)]. Пізніше ця ідея зацікавила інших дослідників, які глибоко вивчали ці простори, а також навели та детально проаналізували деякі інші слабші форми рівномірної опуклості. Згодом ідею рівномірної опуклості та її слабших форм було також поширено на лінійні метричні простори. Протягом багатьох років дослідники вивчали та аналізували властивості лінійних метричних просторів, оснащених рівномірною опуклістю або її слабшими формами, а також їх взаємозв’язки, успадкування цих властивостей фактор-просторами та застосування цих властивостей в багатьох інших областях математики. У цій статті наведено огляд доступної літератури на цю тему для лінійних метричних просторів. Institute of Mathematics, NAS of Ukraine 2025-11-04 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/8145 10.3842/umzh.v77i2.8145 Ukrains’kyi Matematychnyi Zhurnal; Vol. 77 No. 2 (2025); 155–156 Український математичний журнал; Том 77 № 2 (2025); 155–156 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/8145/10343 Copyright (c) 2025 Harpreet K. Grover, Shelly Garg, T. D. Narang |
| spellingShingle | Grover, Harpreet K. Garg, Shelly Narang, T. D. Grover, Harpreet K. Garg, Shelly Narang, T. D. On uniform convexity of linear metric spaces |
| title | On uniform convexity of linear metric spaces |
| title_alt | On uniform convexity of linear metric spaces |
| title_full | On uniform convexity of linear metric spaces |
| title_fullStr | On uniform convexity of linear metric spaces |
| title_full_unstemmed | On uniform convexity of linear metric spaces |
| title_short | On uniform convexity of linear metric spaces |
| title_sort | on uniform convexity of linear metric spaces |
| topic_facet | Linear metric space strictly convex uniformly convex U.C.I/II/III/IV/V. |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8145 |
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