A modified proximal point algorithm for a nearly asymptotically quasi-nonexpansive mapping with an application

In this paper, we introduce a new modified proximal point algorithm based on M-iteration to approximate a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mapping in CAT(0) space. We also prove the $$\Delta $$ -convergence of the proposed algorithm for solving common minimization problem and fixed point problem. We also provide an application and numerical results based on our proposed algorithm.