Generalized projection method for a variational inequality system with different mapping in Banach spaces

The approximate solution of a system for variational inequality with different mapping in Hilbert spaces has been studied, based on the convergence of projection methods. However, little research has been done in Banach space. The primary reason is that projection mapping lacks preferable properties in Banach space. In this paper, we introduce generalized projection methods. By using these methods, the results presented in this paper have extended the main results of Chang et al.’s and Huang and Noor’s recent works [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; Zhenyu Huang, Muhammad Aslam 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] from Hilbert spaces to Banach space.