Department of Mathematics, Institute for Advanced Studies in Studies in Studies in CAT(0) spaces

Abstract

In this paper, we introduced a new mapping given by a finite family of multivalued monotone mappings in a CAT(0) space. We further propose a modied Halpern-type algorithm for the mapping and prove a strong convergence theorem for approximating a common solution of nite family of monotone inclusion problems in a complete CAT(0) space. We also applied our results to solve a nite family of minimization problems in a complete CAT(0) space. Some non-trivial examples of monotone mappings in complete CAT(0) space setting were also studied and a numerical example of our algorithm to further show its applicability is also presented. Our numerical experiment shows that our algorithm converges faster than that proposed in [42] by Takahashi and Shimoji, Mathematical and Computer Modelling 32 (2000), 1463{1471.

Key words: CAT(0) spaces, monotone inclusion problem, monotone operators, W-mapping, xed point, strong convergence.