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

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 gen-eralized resolvent operator technique associated with (A,η)-monotonicity, the approxi-mation 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. Copyright © 2007 Yeol Je Cho et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Introduction an