Systems of generalized nonlinear variational inequalities and its projection methods

Based on relaxed cocoercive monotonicity, a new generalized class of nonlinear variational inequality problems is presented. Our results improve and extend the recent ones announced by [H. Y. Huang, M. A. Noor, An explicit projection method for a system of nonlinear variational inequalities with different (γ,r)(γ,r)-cocoercive mappings, Appl. Math. Comput. 190 (2007) 356–361; S. S. Chang, H. W. Joseph Lee, C. K. Chan, Generalized system for relaxed cocoercive variational inequalities in Hilbert spaces, Appl. Math. Lett. 20 (2007) 329–334; R. U. Verma, Generalized system for relaxed cocoercive variational inequalities and its projection methods, J. Optim. Theory Appl. 121 (2004) 203–210; M. A. Noor, General variational inequalities, Appl. Math. Lett. 1 (1988) 119–121] and many others.