On the strong and $\Delta$-convergence theorems for total asymptotically nonexpansive mappings on CAT(0) space

Abstract

In this paper, we give the strong and $\Delta$-convergence theorems of the modified $S$-iteration and the modified two-step iteration processes for total asymptotically nonexpansive mappings on a CAT(0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature.

Keywords

• cat(0) space
• total asymptotically nonexpansive mapping
• strong convergence
• $\delta$-convergence
• iterative process
• fixed point