New Two-step Viscosity Approximation Methods of Fixed Points for Set-valued Nonexpansive Mappings Associated with Contraction Mappings in CAT(0) Spaces

摘要

The purpose of this paper is to introduce and study a class of new two-step viscosity iteration methods for approximating fixed points of set-valued nonexpansive mappings in CAT(0) spaces. Here, the fixed point is unique solution of a variational inequality with a contraction mapping. Further, we prove strong convergence theorem of the two-step viscosity iterations with some general conditions in a complete CAT(0) space. The presented results improve and unify the corresponding results in the literature.