An accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings with applications to image recovery

Abstract

In this paper, we define a new concept of left and right coordinate affine of a directed graph and then employ it to introduce a new accelerated common fixed point algorithm for a countable family of G-nonexpansive mappings in a real Hilbert space with a graph. We prove, under certain conditions, weak convergence theorems for the proposed algorithm. As applications, we also apply our results to solve convex minimization and image restoration problems. Moreover, we show that our algorithm provides better convergence behavior than other methods in the literature.