Convergence of an Iterative Algorithm for Common Solutions for Zeros of Maximal Accretive Operator with Applications

Abstract

The aim of this paper is to introduce an iterative algorithm for finding a common solution of the sets ${(A+M_2)}^{-1}$(0) and ${(B+M_1)}^{-1}$(0), where M is a maximal accretive operator in a Banach space and, by using the proposed algorithm, to establish some strong convergence theorems for common solutions of the two sets above in a uniformly convex and 2-uniformly smooth Banach space. The results obtained in this paper extend and improve the corresponding results of Qin et al. 2011 from Hilbert spaces to Banach spaces and Petrot et al. 2011. Moreover, we also apply our results to some applications for solving convex feasibility problems.