Davood Afkhami Taba - Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, P.O.Box ۷۹۱۵۸-۹۳۱۴۴, Bandar Abbas, Iran.
Hossein Dehghan - Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Gava Zang, P.O.Box ۴۵۱۳۷-۶۶۷۳۱, Zanjan, Iran

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.

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