Modified Proximal Point Algorithms for Solving Fixed Point Problem and Convex Minimization Problem in Non-Positive Curvature Metric Spaces

Kamonrat Sombut, Nuttapol Pakkaranang, Plerrn Saipara

Abstract

In this paper, we introduce new four steps of proximal point algorithmfor nonexpansive mappings in non-positive curvature metric spaces, namely CAT($0$) spaces and also prove that the sequence generatedby proposed algorithms converges to a minimizer of a convex function and common fixed point of such mappings.