Weak and strong convergence theorems for generalized nonexpansive mappings

Abstract

We consider a class of generalized nonexpansive mappings introduced by Karapinar and seen as a generalization of Suzuki (C)-condition. We prove some weak and strong convergence theorems for approximating fixed points of such mappings under suitable conditions in uniformly convex Banach spaces. Our results generalize those of Khan and Suzuki to the case of this kind of mappings and, in turn, are related to a famous convergence theorem of Reich on nonexpansive mappings. 2016, Universitatii Al.I.Cuza din Iasi. All rights reserved.