On systems of generalized nonlinear variational inequalities in Banach spaces

In this paper, we introduce a new algorithm for a system for generalized nonlinear variational inequalities in Banach spaces by using convergence of the generalized projection methods.Our results extend and improve the results of Fan [J.H. Fan, A Mann type iterative scheme for variational inequalities in noncompact subsets of Banach spaces, J. Math. Anal. Appl. 337 (2007) 1041–1047], Li [J. Li, On the existence of solutions of variational inequalities in Banach spaces, J. Math. Anal. Appl. 295 (2004) 115–126], Verma [R.U. Verma, Projection methods, algorithms and a new system of nonlinear variational inequalities, Comput. Math. Appl. 41 (2001) 1025–1031] and many others.