Generalized Nonlinear Variational Inclusions Involving (A,η)-Monotone Mappings in Hilbert Spaces

Abstract

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.