# A new one-step iterative process for approximating common fixed points of a countable family of quasi-nonexpansive multi-valued mappings in CAT(0) spaces

Document Type : Research Paper

Authors

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

2 Department of Mathematics‎, ‎Faculty of Science and Technology‎, ‎Nakhon Pathom Rajabhat University‎, ‎Nakhon Pathom 73000‎, ‎Thailand‎, ‎and‎ Research Center for Pure and Applied Mathematics‎, ‎Research and‎ ‎Development Institute‎, ‎Nakhon Pathom Rajabhat University‎, ‎Nakhon‎ ‎Pathom 73000‎, ‎Thailand.

Abstract

‎In this paper‎, ‎we propose a new one-step iterative process for a‎ ‎countable family of quasi-nonexpansive multi-valued mappings in a‎ ‎CAT(0) space‎. ‎We also prove strong and $Delta$-convergence theorems‎ ‎of the proposed iterative process under some control conditions‎. ‎Our‎ ‎main results extend and generalize many results in the literature.

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Main Subjects

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### History

• Receive Date: 03 July 2015
• Revise Date: 21 March 2016
• Accept Date: 05 May 2016
• First Publish Date: 01 October 2017