Journal of Inequalities and Applications
Volume 2009 (2009), Article ID 209485, 15 pages
doi:10.1155/2009/209485
Research Article

Mixed Variational-Like Inequality for Fuzzy Mappings in Reflexive Banach Spaces

Poom Kumam1,2 and Narin Petrot2,3

1Department of Mathematics, Faculty of Science, King Mongkuts University of Technology Thonburi, Bang Mod, Bangkok 10140, Thailand
2Centre of Excellence in Mathematics, CHE, Sriayudthaya Road, Bangkok 10400, Thailand
3Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Received 21 April 2009; Accepted 24 July 2009

Academic Editor: Vy Khoi Le

Copyright © 2009 Poom Kumam and Narin Petrot. 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

Some existence theorems for the mixed variational-like inequality for fuzzy mappings (FMVLIP) in a reflexive Banach space are established. Further, the auxiliary principle technique is used to suggest a novel and innovative iterative algorithm for computing the approximate solution. Consequently, not only the existence of solutions of the FMVLIP is shown, but also the convergence of iterative sequences generated by the algorithm is also proven. The results proved in this paper represent an improvement of previously known results.