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International Journal of Mathematics and Mathematical Sciences
Volume 2005, Issue 9, Pages 1415-1420
http://dx.doi.org/10.1155/IJMMS.2005.1415

On solvability of general nonlinear variational-like inequalities in reflexive Banach spaces

1Department of Mathematics, Liaoning Normal University, P.O. Box 200, Liaoning, Dalian 116029, China
2Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 660-701, Korea

Received 28 December 2004

Copyright © 2005 Hindawi Publishing Corporation. 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

We introduce and study a new class of general nonlinear variational-like inequalities in reflexive Banach spaces. By applying a minimax inequality, we establish two existence and uniqueness theorems of solutions for the general nonlinear variational-like inequality.