Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in CAT ( 0 ) $operatorname {CAT}(0)$ spaces

摘要

In this paper, a new modified proximal point algorithm involving fixed point iterates of asymptotically nonexpansive mappings in CAT ( 0 ) $operatorname {CAT}(0)$ spaces is proposed and the existence of a sequence generated by our iterative process converging to a minimizer of a convex function and a common fixed point of asymptotically nonexpansive mappings is proved.