New iterative methods for nonlinear operators as concerns convex programming applicable in differential problems, image deblurring, and signal recovering problems

Abstract

In this paper, using sunny nonexpansive retractions, which are different from the metric projection in Banach spaces, a new type of study regarding the iterative methods in view of two quasi-nonexpansive nonself mappings is presented. We also give the convergence analysis for the proposed method in the background of uniformly convex Banach spaces. Moreover, we apply our results to find solutions of common zeros of accretive operators, convexly constrained least square problems, and convex minimization problems. Furthermore, we also discuss novel applications of these methods to differential problems, image deblurring, and signal recovering problems.

Iteration Scheme for Approximating Fixed Points of G-Nonexpansive Maps on Banach Spaces via a Digraph

“…Many mathematicians have been interested in simulated results for image deblurring and signal recovering problems in recent years, also see e.g. [28][29][30]. The reader on the other hand can apply our proposed method to solve image deblurring and signal recovering problems.…”