Fixed Point Theory and Applications
Volume 2007 (2007), Article ID 29653, 6 pages
doi:10.1155/2007/29653
Generalized Nonlinear Variational Inclusions Involving (A,η)-Monotone Mappings in Hilbert Spaces
Yeol Je Cho1
, Xiaolong Qin2
, Meijuan Shang3
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
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.