Convergence Results on Splitting Operator for Convex Minimization Problem and Its Applications

Duangkamon Kitkuan, Wiyada Kumam

Abstract

The purpose of this paper is to introduce a new iterative method that is a combination of the modified Mann type forward-backward splitting with the  viscosity approximation method and the alternating resolvent method for finding the zero of sum of accretive operators in uniformly convex real Banach spaces which are also uniformly smooth spaces. Our result is new and complements many recent and important results in this direction in the literature. Moreover, we also applied our algorithm to solving the  convex minimization problem for solving image restoration.