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Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-)nonexpansive mappings

Abstract

We study an implicit predictor-corrector iteration process for finitely many asymptotically quasi-nonexpansive self-mappings on a nonempty closed convex subset of a Banach space. We derive a necessary and sufficient condition for the strong convergence of this iteration process to a common fixed point of these mappings. In the case is a uniformly convex Banach space and the mappings are asymptotically nonexpansive, we verify the weak (resp., strong) convergence of this iteration process to a common fixed point of these mappings if Opial's condition is satisfied (resp., one of these mappings is semicompact). Our results improve and extend earlier and recent ones in the literature.

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Correspondence to L. C. Ceng.

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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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Ceng, L.C., Wong, N.C. & Yao, J.C. Implicit predictor-corrector iteration process for finitely many asymptotically (quasi-)nonexpansive mappings. J Inequal Appl 2006, 65983 (2006). https://doi.org/10.1155/JIA/2006/65983

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Keywords

  • Banach Space
  • Convex Subset
  • Nonexpansive Mapping
  • Strong Convergence
  • Iteration Process
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