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  • Research Article
  • Open Access

Fixed point variational solutions for uniformly continuous pseudocontractions in Banach spaces

Fixed Point Theory and Applications20062006:69758

https://doi.org/10.1155/FPTA/2006/69758

  • Received: 27 June 2005
  • Accepted: 28 November 2005
  • Published:

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.

Keywords

  • Differential Geometry
  • Computational Biology
  • Variational Solution

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Authors’ Affiliations

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

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