Strong convergence of new two-step viscosity iterative approximation methods for set-valued nonexpansive mappings in \(\mathrm{CAT}(0)\) spaces (Q725168)

Summary: This paper is for the purpose of introducing and studying a class of new two-step viscosity iteration approximation methods for finding fixed points of set-valued nonexpansive mappings in \(\mathrm{CAT}(0)\) spaces. By means of some properties and characteristic to \(\mathrm{CAT}(0)\) space and using Cauchy-Schwarz inequality and Xu's inequality, strong convergence theorems of the new two-step viscosity iterative process for set-valued nonexpansive and contraction operators in complete \(\mathrm{CAT}(0)\) spaces are provided. The results of this paper improve and extend the corresponding main theorems in the literature.