A new class of generalized nonlinear variational inclusions involving ( A , η ) -monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with ( A , η ) -monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since ( A , η ) -monotonicity generalizes A -monotonicity and H -monotonicity, results obtained in this paper improve and extend many others.