Generalized Nonlinear Variational Inclusions Involving -Monotone Mappings in Hilbert Spaces

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