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Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings

By M. Radhakrishnan and S. Rajesh

Abstract

Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically non expansive maps. Further, Kirk raised the following question: “Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings when ever X has the fixed point property for nonexpansive mappings?”. In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if X  has uniform normal structure or X is uniformly convex in every direction with the Maluta constant D(X) < 1. Also, we study the asymptotic behavior of the sequence {Tnx} for a pointwise eventually asymptotically nonexpansive map T defined on a nonempty weakly compact convex subset K of a Banach space X whenever X satisfies the uniform Opial condition or X has a weakly continuous duality map

Topics: fixed points, pointwise eventually asymptotically nonexpansive mappings, uniform normal structure, uniform Opial condition, duality mappings, Mathematics, QA1-939, Analysis, QA299.6-433
Publisher: Universitat Politècnica de València
Year: 2019
DOI identifier: 10.4995/agt.2019.10360
OAI identifier: oai:doaj.org/article:29eb598e5a8d49c894e0b7e71552d36c
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