Demiclosedness Principle for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Abstract

We prove the demiclosedness principle for a class of mappings which is a generalization of all the forms of nonexpansive, asymptotically nonexpansive, and nearly asymptotically nonexpansive mappings. Moreover, we establish the existence theorem and convergence theorems for modified Ishikawa iterative process in the framework of $CAT(0)$ spaces. Our results generalize, extend, and unify the corresponding results on the topic in the literature.