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Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces

Fixed Point Theory and Applications volume 2006, Article number: 59692 (2006) Cite this article

Abstract

We prove Browder's type strong convergence theorems for infinite families of nonexpansive mappings. One of our main results is the following: let be a bounded closed convex subset of a uniformly smooth Banach space . Let be an infinite family of commuting nonexpansive mappings on . Let and be sequences in satisfying for . Fix and define a sequence in by for . Then converges strongly to , where is the unique sunny nonexpansive retraction from onto .

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  1. Department of Mathematics, Kyushu Institute of Technology, Sensuicho, Kitakyushu, Tobata, 804-8550, Japan

    Tomonari Suzuki

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  1. Tomonari Suzuki
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Correspondence to Tomonari Suzuki.

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Suzuki, T. Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces. Fixed Point Theory Appl 2006, 59692 (2006). https://doi.org/10.1155/FPTA/2006/59692

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