A modified proximal point algorithm in geodesic metric space

Abstract

Proximal point algorithm is one of the most popular technique to find either zero of monotone operator or minimizer of a lower semi-continuous function. In this paper, we propose a new modified proximal point algorithm for solving minimization problems and common fixed point problems in CAT(0) spaces. We prove Δ and strong convergence of the proposed algorithm. Our results extend and improve the corresponding recent results in the literature.

Keywords

• minimization problem
• resolvent operator
• cat(0) space
• proximal point algorithm
• nonexpansive mappings