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Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces

Fixed Point Theory and Applications volume 2004, Article number: 829453 (2004) Cite this article

Abstract

We first introduce an iterative sequence for finding fixed points of relatively nonexpansive mappings in Banach spaces, and then prove weak and strong convergence theorems by using the notion of generalized projection. We apply these results to the convex feasibility problem and a proximal-type algorithm for monotone operators in Banach spaces.

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Authors and Affiliations

  1. Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Oh-Okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Shin-ya Matsushita & Wataru Takahashi

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  1. Shin-ya Matsushita
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  2. Wataru Takahashi
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Correspondence to Shin-ya Matsushita.

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Matsushita, Sy., Takahashi, W. Weak and strong convergence theorems for relatively nonexpansive mappings in Banach spaces. Fixed Point Theory Appl 2004, 829453 (2004). https://doi.org/10.1155/S1687182004310089

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  • DOI: https://doi.org/10.1155/S1687182004310089