Demiclosed principle and ΔΔ-convergence theorems for total asymptotically nonexpansive mappings in CAT(0) spaces

The purpose of this paper is to introduce the concept of total asymptotically nonexpansive mappings and to prove the demiclosed principle   for this kind of mappings in CAT(0) spaces. As a consequence, we obtain a ΔΔ-convergence theorem of the Krasnoselskii–Mann type iteration for total asymptotically nonexpansive mappings in this setting. Our results extend and improve the corresponding recent results announced by many authors.