Convergence of generalized mann type of iterates to common fixed point

Abstract

The present paper deals with the convergence of two modified Mann type of iteration schemes for a single and a finite family of mappings to the fixed and common fixed point, respectively, of a single and a finite family of quasi-nonexpansive mappings on a uniformly convex Banach space. An example is added in support of our main result. The results obtained generalize the earlier results of Rhoades (J Math Anal Appl 56:741–750, [6]), Som et al. (Proc Nat Acad Sci (India) 70(A)(II):185–189, [8]), and others in turn. © Springer Nature Singapore Pte Ltd. 2018.