Three-step Iterations for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

Abstract

In this paper, we establish strong and \Delta$-convergence theorems of modified three-step iterations for total asymptotically nonexpansive mapping which is wider than the class asymptotically nonexpansive mappings in the framework of CAT(0) spaces. Our results extend and generalize the corresponding results of Chang {\it et
al}. [Demiclosed principle and $\Delta$-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces, Appl. Math. Comput. 219(5)(2012), 2611-2617], Nanjaras and Panyanak [Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces, Fixed Point Theory Appl. Vol. 2010, Art. ID 268780],
and many others.