Common Fixed Points for Nonexpansive Mappings and Nonspreading Mappings in Banach Spaces

Abstract

In this thesis, firstly, we prove the existence of a common fixed point for firmly nonspreading mappings and quasi-nonexpansive mappings in CAT(0) spaces. Secondly, we introduce an iterative scheme by using the concept of Ishikawa iterative scheme and prove ∆ - convergence theorems for firmly nonspreading mappings and quasi-nonexpansive mappings in CAT(0) spaces. Finally, we introduce an iterative scheme by viscosity approximation method related to the previous method for obtaining a strong convergence theorem for a common fixed point of a family of nonexpansive mappings in a real Hilbert space.