Sitthithakerngkiet, K., Sunthrayuth, P., Kumam, P. (2017). Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces. Bulletin of the Iranian Mathematical Society, 43(1), 239-258.

K. Sitthithakerngkiet; P. Sunthrayuth; P. Kumam. "Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces". Bulletin of the Iranian Mathematical Society, 43, 1, 2017, 239-258.

Sitthithakerngkiet, K., Sunthrayuth, P., Kumam, P. (2017). 'Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces', Bulletin of the Iranian Mathematical Society, 43(1), pp. 239-258.

Sitthithakerngkiet, K., Sunthrayuth, P., Kumam, P. Some iterative method for finding a common zero of a finite family of accretive operators in Banach spaces. Bulletin of the Iranian Mathematical Society, 2017; 43(1): 239-258.

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

^{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.

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

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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