Iterative algorithm for a family of monotone inclusion problems in cat(0) spaces

Abstract

In this paper, we introduce a new mapping given by a finite family of multivalued monotone mappings in a CAT(0) space. We further propose a modified Halpern-type algorithm for the mapping and prove a strong convergence theorem for approximating a common solution of finite family of monotone inclusion problems in a complete CAT(0) space. We also applied our results to solve a finite 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.