A novel iterative scheme of operators with property (E) and its applications

Abstract

The goal of this note is to propose a new iterative scheme for finding the fixed points of generalized nonexpansive mappings with property (E), called MCS-iteration. We prove both weak and strong convergence properties in a uniformly convex Banach space. Furthermore, an application of signal recovery in a compressed sensing problem is shown as numerical examples of the iterative scheme.