# Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces

Document Type: Research Paper

Authors

1 Nonlinear Dynamic Analysis Research Center‎, ‎Department of Mathematics‎, ‎Faculty of Applied Science‎, ‎King Mongkut's University of Technology North Bangkok (KMUTNB)‎, ‎1518‎, ‎Pracharat 1 Road‎, ‎Wongsawang‎, ‎Bangsue‎, ‎Bangkok‎, ‎10800‎, ‎Thailand

2 KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA)‎, ‎Theoretical and Computational Science Center (TaCS)‎, ‎Science Laboratory Building‎, ‎Faculty of Science‎, ‎King Mongkuts University of Technology Thonburi (KMUTT)‎, ‎126 Pracha Uthit Road‎, ‎Bang Mod‎, ‎Thung Khru‎, ‎Bangkok‎, ‎10140‎, ‎Thailand.

3 Department of Medical Research‎, ‎China Medical University Hospital‎, ‎China Medical University‎, ‎Taichung 40402‎, ‎Taiwan.

Abstract

‎The purpose of this paper is to introduce a new mapping for a finite‎ ‎family of accretive operators and introduce an iterative algorithm‎ ‎for finding a common zero of a finite family of accretive operators‎ ‎in a real reflexive strictly convex Banach space which has a‎ ‎uniformly G\^ateaux differentiable norm and admits the duality‎ ‎mapping $j_{\varphi}$‎, ‎where $\varphi$ is a gauge function invariant‎ ‎on $[0,\infty)$‎. ‎Furthermore‎, ‎we prove the strong convergence under‎ ‎some certain conditions‎. ‎The results obtained in this paper improve‎ ‎and extend the corresponding ones announced by many others‎.

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Main Subjects

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### History

• Receive Date: 27 February 2013
• Revise Date: 24 August 2015
• Accept Date: 08 November 2015