Common Fixed Points of Generalized α-Nonexpansive Multivalued Mappings via Modified S-Type Iteration

Abstract

In this paper, we introduce a class of generalized α-nonexpansive multivalued mapping and study some of its important properties. In particular, this class is a multivalued version of the single-valued nonexpansive mapping, called generalized α-nonexpansive mapping proposed by Pant and Shukla [11]. A modified S-type iteration scheme is proposed to approximate the common fixed point of two multivalued mappings. Our algorithm provides a multivalued extension of the method given by Khan et al. [6]. Strong and weak convergence of the iterative process are also proved under suitable assumptions.