Numerical Reckoning Fixed Points for Nonexpansive Mappings via a Faster Iteration Process and Its Application to Constrained Minimization Problems, Split Feasibility Problems and Image Deblurring Problems

Chonjaroen Chairatsiripong, Damrongsak Yambangwai, Tanakit Thianwan

Abstract

In this paper, we introduce a new faster iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that our iteration process is faster than a number of existing iteration processes.  We support our analytic proof by  numerical examples in which we approximate the fixed point by a computer using Matlab program. Furthermore, we apply our results to find solutions of constrained minimization problems, split feasibility problems and image deblurring problems. Our results are the extension, improvement and generalizationof many known results in the literature of iterations in fixed point theory.