Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 467512, 12 pages
doi:10.1155/2009/467512
Research Article

On Solvability of a Generalized Nonlinear Variational-Like Inequality

Zeqing Liu,1 Pingping Zheng,1 Jeong Sheok Ume,2 and Shin Min Kang3

1Department of Mathematics, Liaoning Normal University, Dalian, Liaoning 116029, China
2Department of Applied Mathematics, Changwon National University, Changwon 641-773, South Korea
3Department of Mathematics, The Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, South Korea

Received 12 July 2009; Accepted 28 September 2009

Academic Editor: Vy Khoi Le

Copyright © 2009 Zeqing Liu 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.

Abstract

A new generalized nonlinear variational-like inequality is introduced and studied. By applying the auxiliary principle technique and KKM theory, we construct a new iterative algorithm for solving the generalized nonlinear variational-like inequality. By means of the Banach fixed-point theorem, we establish the existence and uniqueness of solution for the generalized nonlinear variational-like inequality. The convergence of the sequence generated by the iterative algorithm is also discussed.