Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces

Abstract

Recently, Reich and Zaslavski have studied a new inexact iterative scheme for fixed points of contractive and nonexpansive multifunctions. In 2011, Aleomraninejad, et. al. generalized some of their results to Suzuki-type multifunctions.  The study of iterative schemes for various classes of contractive and nonexpansive mappings is a central topic in fixed point theory. The importance of Banach contraction principle is that it also gives the convergence of an iterative scheme to a unique fixed point. In this paper,  we consider $(X, M, *)$ to be fuzzy metric spaces in Park's sense and we show our results for fixed points of contractive and nonexpansive multifunctions on Hausdorff fuzzy metric space.