Fixed points of asymptotically nonexpansive mappings with center 0 and applications

2021/03/19 by Abdelkader Dehici, Dehici, Abdelkader, Sami Atailia +2
Computer Science · Engineering · Mathematics · #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA) #General Topology (math.GN) #Nonlinear Differential Equations Analysis #Optimization and Variational Analysis #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2103.10727

openalex publication_date 2021/03/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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