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Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces

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Published/Copyright: June 7, 2010
Journal of Applied Analysis
From the journal Journal of Applied Analysis Volume 7 Issue 2

Abstract

Let K be a closed convex subset of a Banach space X and let F be a nonempty closed convex subset of K. We consider complete metric spaces of self-mappings of K which fix all the points of F and are relatively nonexpansive with respect to a given convex function ƒ on X. We prove (under certain assumptions on ƒ) that the iterates of a generic mapping in these spaces converge strongly to a retraction onto F.

Key words and phrases.: Bregman distance; convex function; fixed point; generic property; iterative algorithm; uniform space
Received: 2000-11-13
Published Online: 2010-06-07
Published in Print: 2001-December

© Heldermann Verlag

Articles in the same Issue

  1. Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
  2. Exceptional Sets for Universally Polygonally Approximable Functions
  3. Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
  4. The Nevanlinna Theorem of the Classical Theory of Moments Revisited
  5. Measures in Locally Compact Groups are Carried by Meager Sets
  6. On Sequences of Upper and Lower Semi-Quasicontinuous Functions
  7. Compositions of Sierpiński-Zygmund Functions and Related Combinatorial Cardinals
  8. Gradient-Finite Element Method for Nonlinear Neumann Problems
  9. On Sets Determined by Sequences of Quasi-Continuous Functions
  10. On Minimal Pairwise Sufficient Statistics
https://doi.org/10.1515/JAA.2001.151
Keywords for this article
Bregman distance; convex function; fixed point; generic property; iterative algorithm; uniform space

Articles in the same Issue

  1. Asymptotic Behavior of Relatively Nonexpansive Operators in Banach Spaces
  2. Exceptional Sets for Universally Polygonally Approximable Functions
  3. Some Remarks on Nonuniqueness of Minimizers for Discrete Minimization Problems
  4. The Nevanlinna Theorem of the Classical Theory of Moments Revisited
  5. Measures in Locally Compact Groups are Carried by Meager Sets
  6. On Sequences of Upper and Lower Semi-Quasicontinuous Functions
  7. Compositions of Sierpiński-Zygmund Functions and Related Combinatorial Cardinals
  8. Gradient-Finite Element Method for Nonlinear Neumann Problems
  9. On Sets Determined by Sequences of Quasi-Continuous Functions
  10. On Minimal Pairwise Sufficient Statistics
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