On a proximal point algorithm for solving common fixed point problems and convex minimization problems in Geodesic spaces with positive curvature

Abstract

In this article, we present a new modified proximal point algorithm in the framework of CAT(1) spaces which is utilized for solving common fixed point problem and minimization problems. Also, we prove convergence results of the obtained process under some mild conditions. Our results extend and improve several corresponding results of the existing literature.

Keywords

• minimization problem
• resolvent operator
• cat(1) space
• proximal point algorithm
• nonexpansive mapping