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Mathematics > Functional Analysis
Title: Fixed points of asymptotically nonexpansive mappings with center 0 and applications
(Submitted on 19 Mar 2021 (v1), last revised 12 May 2024 (this version, v2))
Abstract: 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.
Submission history
From: Sami Atailia [view email][v1] Fri, 19 Mar 2021 10:50:44 GMT (16kb)
[v2] Sun, 12 May 2024 21:15:19 GMT (16kb)
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