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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 310369, 19 pages
http://dx.doi.org/10.1155/2012/310369
Research Article

Vectorial Ekeland Variational Principles and Inclusion Problems in Cone Quasi-Uniform Spaces

1School of Mathematical Science, Xuzhou Normal University, Xuzhou 221116, China
2Department of Mathematics and the RINS, Gyeongsang National University, Chinju 660-701, Republic of Korea
3Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou 730050, China

Received 2 December 2011; Revised 23 February 2012; Accepted 5 March 2012

Academic Editor: D. O'Regan

Copyright © 2012 Jiang Zhu 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

Some new vectorial Ekeland variational principles in cone quasi-uniform spaces are proved. Some new equivalent principles, vectorial quasivariational inclusion principle, vectorial quasi-optimization principle, vectorial quasiequilibrium principle are obtained. Also, several other important principles in nonlinear analysis are extended to cone quasi-uniform spaces. The results of this paper extend, generalize, and improve the corresponding results for Ekeland's variational principles of the directed vectorial perturbation type and other generalizations of Ekeland's variational principles in the setting of F-type topological space and quasi-metric spaces in the literatures. Even in usual real metric spaces, some of our results are new.