On A Proximal-Point Algorithm For Solving the Minimization Problem and Common Fixed-Point Problem in Cat(k) Spaces

We propose a new modified proximal-point algorithm in the setting of CAT(1) spaces, which can be used to solve the minimization problem and the common fixed-point problem. In addition, we prove several convergence results for the proposed algorithm under certain mild conditions. Further, we provide some applications for the convex minimization problem and the fixed-point problem in the CAT(k) spaces with a bounded positive real number k. In the process, several relevant results available in the existing literature are generalized and improved.