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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Global iteration schemes for strongly pseudo-contractive maps
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by C. E. Chidume PDF
Proc. Amer. Math. Soc. 126 (1998), 2641-2649 Request permission

Abstract:

Suppose $E$ is a real uniformly smooth Banach space, $K$ is a nonempty closed convex and bounded subset of $E$, and $T:K\to K$ is a strong pseudo-contraction. It is proved that if $T$ has a fixed point in $K$ then both the Mann and the Ishikawa iteration processes, for an arbitrary initial vector in $K$, converge strongly to the unique fixed $T$. No continuity assumption is necessary for this convergence. Moreover, our iteration parameters are independent of the geometry of the underlying Banach space and of any property of the operator.
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Additional Information
  • C. E. Chidume
  • Affiliation: International Centre for Theoretical Physics, 34100 Trieste, Italy
  • MR Author ID: 232629
  • Email: chidume@ictp.trieste.it
  • Received by editor(s): April 22, 1996
  • Received by editor(s) in revised form: January 27, 1997
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1998 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 126 (1998), 2641-2649
  • MSC (1991): Primary Primnary, 47H17, 47H06, 47H15
  • DOI: https://doi.org/10.1090/S0002-9939-98-04322-6
  • MathSciNet review: 1451791