A New faster Iteration Process to fixed points of mean-non expansive Mappings in Banach Space

Abstract

Let X be a Banach space and F a subset of X. In this paper, we introduce a new iterative scheme to approximate fixed point of mean non-expansive mappings. We first prove that proposed iteration process is faster than all of Mann, Ishikawa, Picard, Agarwal, Noor and Thakur processes for contractive mappings. We also show that some weak and strong convergence theorems for mean non-expansive mappings. Using example presented in mean non-expansive mappings in Banach space. We compare the convergence behavior of the new iterative process with other iterative processes. Keywords. Mean non-expansive mappings, Iterative Process, Uniformly Convex Banach Space, Convergence Theorem.