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Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Applied Mathematics-A Journal of Chinese Universities Springer Journals

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

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Publisher
Springer Journals
Copyright
Copyright © 2008 by Editorial Committee of Applied Mathematics-A Journal of Chinese Universities and Springer-Verlag GmbH
Subject
Mathematics; Applications of Mathematics; Mathematics, general
ISSN
1005-1031
eISSN
1993-0445
DOI
10.1007/s11766-008-1951-9
Publisher site
See Article on Publisher Site

Abstract

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.

Journal

Applied Mathematics-A Journal of Chinese Universities – Springer Journals

Published: Sep 7, 2008

References

  • A strong convergence theorem for relatively nonexpansive mappings in a Banach space
    Matsushita, S.; Takahashi, W.
  • Strong convergence theorems for relatively nonexpansive mappings in a Banach space
    Qin, X. L.; Su, Y. F.
  • Strong convergence of the CQ method for fixed point iteration processes
    Martinez-Yanes, C.; Xu, H. K.
  • Forcing strong convergence of proximal point iterations in a Hilbert space
    Solodov, M. V.; Svaiter, B. F.
  • Nonlinear Functional Analysis
    Takahashi, W.
  • Nonlinear Mappings of Monotone Type
    Pascali, D.; Sburlan, S.
  • Theory and Applications of Nonlinear Operators of Accretive and Monotone Type
    Alber, Y. I.
  • Strong convergence of a proximal-type algorithm in a Banach space
    Kamimura, S.; Takahashi, W.