Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 029653, 6 pages
doi:10.1155/2007/29653
Research Article

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

Yeol Je Cho,1 Xiaolong Qin,2 Meijuan Shang,3 and Yongfu Su4

1Department of Mathematics Education and the RINS, Gyeongsang National University, Chinju 660-701, South Korea
2Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Korea
3Department of Mathematics, Shijiazhuang University, Shijiazhuang 050035, China
4Department of Mathematics, Tianjin Polytechnic University, Tianjin 300160, China

Received 30 July 2007; Accepted 12 November 2007

Academic Editor: Mohamed Amine Khamsi

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.

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.