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Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces

Fixed Point Theory and Applications volume 2006, Article number: 69758 (2006) Cite this article

Abstract

Let be a reflexive Banach space with a uniformly Gâteaux differentiable norm, let be a nonempty closed convex subset of , and let be a uniformly continuous pseudocontraction. If is any contraction map on and if every nonempty closed convex and bounded subset of has the fixed point property for nonexpansive self-mappings, then it is shown, under appropriate conditions on the sequences of real numbers , , that the iteration process , , , strongly converges to the fixed point of , which is the unique solution of some variational inequality, provided that is bounded.

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Authors and Affiliations

  1. Department of Mathematics, Statistics, & Computer Science, University of Port Harcourt, Port Harcourt, PMB 5323, Nigeria

    Aniefiok Udomene

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  1. Aniefiok Udomene
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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Udomene, A. Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces. Fixed Point Theory Appl 2006, 69758 (2006). https://doi.org/10.1155/FPTA/2006/69758

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