On the Monotone Mappings in CAT(0) Spaces

Abstract

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(0) metric spaces.

Keywords

• monotone mapping
• nonexpansive mapping
• variational inequality
• fixed point
• cat(0) metric space