Convergence of an Iterative Scheme for Multifunctions on Fuzzy Metric Spaces

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 Suzukitype 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.