Some Convergence Theorems of Modified Proximal Point Algorithms for Nonexpansive Mappings in CAT(0) Spaces

Abstract

In this paper, a new modified proximal point algorithm is proposed for finding a common element of the set of fixed points of a single-valued nonexpansive mapping, and the set of fixed points of a multivalued nonexpansive mapping, and the set of minimizers of convex and lower semicontinuous functions. We obtain convergence of the proposed algorithm to a common element of three sets in CAT(0) spaces.

Keywords

• cat(0) space
• proximal point algorithm
• fixed point
• resolvent identity
• functional analysis