Proximal point algorithms involving fixed points of nonexpansive mappings in CAT ( 0 ) $\operatorname{CAT}(0)$ spaces

In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in $\operatorname{CAT}(0)$ spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings.