Convergence theorems for total asymptotically nonexpansive mappings in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces

Abstract

Abstract The purpose of this paper is to study the convergence theorems in CAT ( κ ) $\operatorname{CAT} (\kappa )$ spaces with k > 0 $k > 0$ for total asymptotically nonexpansive mappings which are essentially wider than nonexpansive mappings, asymptotically nonexpansive mapping, and asymptotically nonexpansive mappings in the intermediate sense. Our results generalize, unify, and improve several comparable results in the existing literature.

Keywords

• Total asymptotically nonexpansive mappings
• CAT ( κ ) $\operatorname{CAT} (\kappa )$ space
• k > 0 $k > 0$
• Demiclosedness principle
• Asymptotically nonexpansive mapping in the intermediate sense
• Asymptotically nonexpansive mapping