Strict Convexity and Uniform Convexity in Linear 2-normed Spaces
Linear 2-normed space is a generalization of linear normed space, which defines a more extensive norm. In this paper, we get contraction mapping theorem in linear 2-normed space holds, and the set of fixed points for nonexpansive mapping is convex when linear 2-normed space is strictly convex. We ob...
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Harbin University of Science and Technology Publications
2021-12-01
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| Series: | Journal of Harbin University of Science and Technology |
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| Online Access: | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2048 |
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| author | LI Shan-shan CUI Yun-an |
| author_facet | LI Shan-shan CUI Yun-an |
| author_sort | LI Shan-shan |
| collection | DOAJ |
| description | Linear 2-normed space is a generalization of linear normed space, which defines a more extensive norm. In this paper, we get contraction mapping theorem in linear 2-normed space holds, and the set of fixed points for nonexpansive mapping is convex when linear 2-normed space is strictly convex. We obtain that the strictly convex linear 2-normed space with finite dimension is uniformly convex. Thus we get the corollary that the linear 2-normed space induced by the vector product is uniformly convex. |
| format | Article |
| id | doaj-art-5cb6eafbf0dc4514bfc1ae4c573617c5 |
| institution | Kabale University |
| issn | 1007-2683 |
| language | zho |
| publishDate | 2021-12-01 |
| publisher | Harbin University of Science and Technology Publications |
| record_format | Article |
| series | Journal of Harbin University of Science and Technology |
| spelling | doaj-art-5cb6eafbf0dc4514bfc1ae4c573617c52025-08-20T03:56:19ZzhoHarbin University of Science and Technology PublicationsJournal of Harbin University of Science and Technology1007-26832021-12-01260615315610.15938/j.jhust.2021.06.021Strict Convexity and Uniform Convexity in Linear 2-normed SpacesLI Shan-shan0CUI Yun-an1School of Sciences, Harbin University of Science and Technology, Harbin 150080, ChinaSchool of Sciences, Harbin University of Science and Technology, Harbin 150080, ChinaLinear 2-normed space is a generalization of linear normed space, which defines a more extensive norm. In this paper, we get contraction mapping theorem in linear 2-normed space holds, and the set of fixed points for nonexpansive mapping is convex when linear 2-normed space is strictly convex. We obtain that the strictly convex linear 2-normed space with finite dimension is uniformly convex. Thus we get the corollary that the linear 2-normed space induced by the vector product is uniformly convex.https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2048linear 2-normed spacecontraction mapping theoremfixed pointstrict convexityuniform convexity |
| spellingShingle | LI Shan-shan CUI Yun-an Strict Convexity and Uniform Convexity in Linear 2-normed Spaces Journal of Harbin University of Science and Technology linear 2-normed space contraction mapping theorem fixed point strict convexity uniform convexity |
| title | Strict Convexity and Uniform Convexity in Linear 2-normed Spaces |
| title_full | Strict Convexity and Uniform Convexity in Linear 2-normed Spaces |
| title_fullStr | Strict Convexity and Uniform Convexity in Linear 2-normed Spaces |
| title_full_unstemmed | Strict Convexity and Uniform Convexity in Linear 2-normed Spaces |
| title_short | Strict Convexity and Uniform Convexity in Linear 2-normed Spaces |
| title_sort | strict convexity and uniform convexity in linear 2 normed spaces |
| topic | linear 2-normed space contraction mapping theorem fixed point strict convexity uniform convexity |
| url | https://hlgxb.hrbust.edu.cn/#/digest?ArticleID=2048 |
| work_keys_str_mv | AT lishanshan strictconvexityanduniformconvexityinlinear2normedspaces AT cuiyunan strictconvexityanduniformconvexityinlinear2normedspaces |