Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings

Authors

  • M. Radhakrishnan University of Madras
  • S. Rajesh Indian Institute of Technology

DOI:

https://doi.org/10.4995/agt.2019.10360

Keywords:

fixed points, pointwise eventually asymptotically nonexpansive mappings, uniform normal structure, uniform Opial condition, duality mappings

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.

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Author Biographies

M. Radhakrishnan, University of Madras

Ramanujan Institute for Advanced Study in Mathematics

S. Rajesh, Indian Institute of Technology

Department of Mathematics

References

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Published

2019-04-01

How to Cite

[1]
M. Radhakrishnan and S. Rajesh, “Existence ofixed points for pointwise eventually asymptotically nonexpansive mappings”, Appl. Gen. Topol., vol. 20, no. 1, pp. 119–133, Apr. 2019.

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