Abstract: A new class of g-η-Monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-Monotone mappings are introduced. The resolvent operator of g-η-Monotone mappings is defined and its Lipschitz continuity is presented. An iterative algorithm for approximating the solutions of generalized implicit variational-like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved.

Key words: g-η-Monotone mapping, resolvent operator, generalized implicit variational-like inclusion, iterative algorithm