Summary: 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 J. H. Fan [J. Math. Anal. Appl. 337, No. 2, 1041–1047 (2008; Zbl 1140.49011)], J. Li [J. Math. Anal. Appl. 295, No. 1, 115–126 (2004; Zbl 1045.49008)], R. U. Verma [Comput. Math. Appl. 41, No. 7–8, 1025–1031 (2001; Zbl 0995.47042)] and many others.