New Modified Proximal Point Algorithm for Solving Minimization and Common Fixed Point Problem over CAT(κ) Spaces

In this paper, we present a newly proximal point algorithm for solving minimization and common fixed point problems in CAT(1) spaces. Under some mild conditions, we prove strong and ∆-convergence theorems. Additionally, a convex minimization application and a common fixed point problems in CAT(κ) spaces with the bounded κ ∈ (0, ∞) are provided. Our findings complement and advance the pertinent recent findings in the literature