In this paper, we propose a new modified proximal point algorithm involving fixed point iteration for nonexpansive mappings in CAT(1) spaces. Under some mild conditions, we prove that the sequence generated by our iterative algorithm \Delta-converges to a common solution between certain convex optimization and fixed point problems.


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Chaipunya, Parin, Cholamjiak, Prasit, Kumam, Poom, Pakkaranang, Nuttapol, Suparatulatorn, Raweerote