Strong Convergence Theorems for Common Points of a Finite Family of Accretive Operators

Jae Ug Jeong∗; Soo Hwan Kim

doi:10.5666/KMJ.2019.59.3.445

Article

KYUNGPOOK Math. J. 2019; 59(3): 445-464

Published online September 23, 2019

Strong Convergence Theorems for Common Points of a Finite Family of Accretive Operators

Jae Ug Jeong∗ and Soo Hwan Kim

Department of Mathematics, Dongeui University, Pusan 47340, South Korea
e-mail : jujeong@deu.ac.kr and sh-kim@deu.ac.kr

Received: March 18, 2016; Revised: June 25, 2019; Accepted: August 5, 2019

Abstract

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Abstract

In this paper, we propose a new iterative algorithm generated by a finite family of accretive operators in a q-uniformly smooth Banach space. We prove the strong convergence of the proposed iterative algorithm. The results presented in this paper are interesting extensions and improvements of known results of Qin et al. [Fixed Point Theory Appl. 2014(2014): 166], Kim and Xu [Nonlinear Anal. 61(2005), 51–60] and Benavides et al. [Math. Nachr. 248(2003), 62–71].