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Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces

Abstract

The convex feasibility problem (CFP) of finding a point in the nonempty intersection is considered, where is an integer and the 's are assumed to be convex closed subsets of a Banach space . By using hybrid iterative methods, we prove theorems on the strong convergence to a common fixed point for a finite family of relatively nonexpansive mappings. Then, we apply our results for solving convex feasibility problems in Banach spaces.

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Correspondence to Somyot Plubtieng.

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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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Plubtieng, S., Ungchittrakool, K. Hybrid Iterative Methods for Convex Feasibility Problems and Fixed Point Problems of Relatively Nonexpansive Mappings in Banach Spaces. Fixed Point Theory Appl 2008, 583082 (2009). https://doi.org/10.1155/2008/583082

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Keywords

  • Banach Space
  • Iterative Method
  • Differential Geometry
  • Nonexpansive Mapping
  • Computational Biology