Open Access

Applications of W. A. Kirk's fixed-point theorem to generalized nonlinear variational-like inequalities in reflexive Banach spaces

Journal of Inequalities and Applications20052005:634163

https://doi.org/10.1155/JIA.2005.251

Received: 10 September 2003

Published: 11 July 2005

Abstract

We introduce and study a new class of generalized nonlinear variational-like inequalities, which includes these variational inequalities and variational-like inequalities due to Bose, Cubiotti, Dien, Ding, Ding and Tarafdar, Noor, Parida, Sahoo, and Kumar, and Yao, and others as special cases. By applying Kirk's fixed-point theorem and Ding-Tan minimax inequality, we establish the existence theorems of solutions for the generalized nonlinear variational-like inequalities in reflexive Banach spaces.

Authors’ Affiliations

(1)
Department of Mathematics, Liaoning Normal University
(2)
Department of Applied Mathematics, College of Natural Sciences, Changwon National University
(3)
Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University

Copyright

© Liu et al. 2005