Fixed points of asymptotically nonexpansive mappings with center 0 and applications
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arXiv
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| Format: | Preprint |
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2021
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| _version_ | 1866909198233632768 |
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| author | Dehici, Abdelkader Atailia, Sami Redjel, Najeh |
| author_facet | Dehici, Abdelkader Atailia, Sami Redjel, Najeh |
| contents | In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results refine those concerning alternate convexically nonexpansive (in short; ACN) mappings studied by P. N. Dowling in " On a fixed point result of Amini-Harandi in strictly convex Banach spaces, Acta. Math. Hungar., 112 (1-2), (2006), 85-88" . Secondly, by using Lau's result in " Closed convex invariant subsets of $L_p(G)$, Trans. Amer. Math. Soc., {\bf 232}, (1977), 131-142", we give another characterization for the noncompactness of locally compact groups $G$. Finally, we discuss the existence of a solution for a nonlinear transport equation without using compactness results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2103_10727 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Fixed points of asymptotically nonexpansive mappings with center 0 and applications Dehici, Abdelkader Atailia, Sami Redjel, Najeh Functional Analysis General Topology In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results refine those concerning alternate convexically nonexpansive (in short; ACN) mappings studied by P. N. Dowling in " On a fixed point result of Amini-Harandi in strictly convex Banach spaces, Acta. Math. Hungar., 112 (1-2), (2006), 85-88" . Secondly, by using Lau's result in " Closed convex invariant subsets of $L_p(G)$, Trans. Amer. Math. Soc., {\bf 232}, (1977), 131-142", we give another characterization for the noncompactness of locally compact groups $G$. Finally, we discuss the existence of a solution for a nonlinear transport equation without using compactness results. |
| title | Fixed points of asymptotically nonexpansive mappings with center 0 and applications |
| topic | Functional Analysis General Topology |
| url | https://arxiv.org/abs/2103.10727 |