Strong Convergence Theorem for Finding a Common Solution of Convex Minimization and Fixed Point Problems in CAT(0) Spaces

Abstract

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems fork-demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm.