Common Attractive Point Theorems for a Finite Family of Multivalued Nonexpansive Mappings in Banach Spaces

Abstract

Our main purpose of this paper is to introduce the modified Mann and Ishikawa iterates for finding a common attractive point of a finite family of multivalued nonexpansive mappings in the setting of uniformly convex Banach spaces. We obtain necessary and sufficient conditions to guarantee the strong convergence of the proposed algorithms without closedness of the domain of such mappings. Moreover, we derive some consequences from our main result to fixed point result of such mappings. Finally, the numerical results are provided to support our main theorem.