△-Convergence Problems for Asymptotically Nonexpansive Mappings in CAT(0)‎ Spaces

Abstract EN

New △-convergence theorems of iterative sequences for asymptotically nonexpansive mappings in CAT(0) spaces are obtained.

Consider an asymptotically nonexpansive self-mapping T of a closed convex subset C of a CAT(0) space X.

Consider the iteration process {xn}, where x0∈C is arbitrary and xn+1=αnxn⊕(1-αn)Tnyn or xn+1=αnTnxn⊕(1-αn)yn,yn=βnxn⊕(1-βn)Tnxn for n≥1, where {αn},{βn}⊂(0,1).

It is shown that under certain appropriate conditions on αn,βn,{xn} △-converges to a fixed point of T.