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An approximation method for common fixed points of a finite family of asymptotic pointwise nonexpansive mappings

Bancha Nanjaras1 and Bancha Panyanak1,2*

Author Affiliations

1 Department of Mathematics, Faculty of Science, Chaing Mai University, Chiang Mai, 50200, Thailand

2 Centre of Excellence in Mathematics, CHE, Si Ayutthaya Rd., Bangkok, 10400, Thailand

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Fixed Point Theory and Applications 2012, 2012:108 doi:10.1186/1687-1812-2012-108

Published: 2 July 2012

Abstract

In this article, we consider an iterative scheme to approximate a common fixed point for a finite family of asymptotic pointwise nonexpansive mappings. We obtain weak and strong convergence theorems of the proposed iteration in uniformly convex Banach spaces. The related results for complete CAT(0) spaces are also included.

MSC: 47H09, 47H10.

Keywords:
common fixed point; asymptotic pointwise nonexpansive mapping; weak convergence; strong convergence; Banach space; CAT(0) space