Fixed Point Theory and Applications
Volume 2009 (2009), Article ID 609353, 9 pages
doi:10.1155/2009/609353

The solvability of a new system of nonlinear variational-like inclusions

Zeqing Liu1 , Min Liu1 , Jeong Sheok Ume3 and Shin Min Kang4

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian Liaoning 116029, China
 3Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea
 4Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea

Abstract

We introduce and study a new system of nonlinear variational-like inclusions involving s-(G,η)-maximal monotone operators, strongly monotone operators, η-strongly monotone operators, relaxed monotone operators, cocoercive operators, (λ,ξ)-relaxed cocoercive operators, (ζ,φ,ϱ)-g-relaxed cocoercive operators and relaxed Lipschitz operators in Hilbert spaces. By using the resolvent operator technique associated with s-(G,η)-maximal monotone operators and Banach contraction principle, we demonstrate the existence and uniqueness of solution for the system of nonlinear variational-like inclusions. The results presented in the paper improve and extend some known results in the literature.