Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 276294, 15 pages
doi:10.1155/2010/276294
Research Article

Vectorial Form of Ekeland-Type Variational Principle in Locally Convex Spaces and Its Applications

S. Eshghinezhad and M. Fakhar

Department of Mathematics, Faculty of Sciences, University of Isfahan, Isfahan 81745-163, Iran

Received 23 June 2010; Accepted 2 November 2010

Academic Editor: A. T M. Lau

Copyright © 2010 S. Eshghinezhad and M. Fakhar. 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

By using a Dane ̆ s ' drop theorem in locally convex spaces we obtain a vectorial form of Ekeland-type variational principle in locally convex spaces. From this theorem, we derive some versions of vectorial Caristi-Kirk's fixed-point theorem, Takahashi's nonconvex minimization theorem, and Oettli-Théra's theorem. Furthermore, we show that these results are equivalent to each other. Also, the existence of solution of vector equilibrium problem is given.