International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 36278, 15 pages
Existence of solutions for generalized nonlinear mixed variational-like inequalities in Banach spaces
1Department of Applied Mathematics, Dalian University of Technology, Dalian, Liaoning 116024, China
2Department of Mathematics, Liaoning Normal University, P.O. Box 200, Dalian, Liaoning 116029, China
3Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, Korea
Received 26 April 2005; Revised 5 December 2005; Accepted 18 December 2005
Copyright © 2006 Yali Zhao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We introduce and study a new class of generalized nonlinear mixed variational-like inequalities in reflexive Banach spaces. By applying Ding's technique we prove several existence and uniqueness theorems of solutions for the generalized nonlinear mixed variational-like inequality, extend the auxiliary problem technique to suggest and analyze an iterative method to compute the approximate solutions of the generalized nonlinear mixed variational-like inequality, and establish the convergence criteria of the iterative method. The results presented in this paper improve, extend, and unify many known results in this area.