Existence and approximation of common fixed points of two mappings in a class of generalized nonexpansive mappings on Banach space

Abstract

In this paper, we introduce the generalized Suzuki type nonexpansive mappings and study existence and approximation of common fixed point of this class of generalized nonexpansive mappings. We use the three step iteration process of Abbas-Nazir for two mappings satisfying the generalized Suzuki type nonexpansive on nonempty subset of a Banach space. We prove some results related to strong and weak convergence of the iteration scheme to get the common fixed point of two mappings satisfying the generalized Suzuki type nonexpansive. Finally, we give an example of two mappings satisfying the given conditions.