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

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.

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