On the Monotone Mappings in CAT(۰) Spaces

In this paper, we first introduce a monotone mapping and its resolvent in general metric spaces.Then, we give two new iterative methods  by combining the resolvent method with Halpern s iterative method and viscosity approximation method for  finding a fixed point of monotone mappings and a solution of variational inequalities. We prove convergence theorems of the proposed iterations  in CAT(۰) metric spaces.

Keywords:

Monotone mapping , Nonexpansive mapping , Variational inequality , Fixed point , CAT(۰) metric space