Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 175453, 35 pages
doi:10.1155/2010/175453
Research Article

Maximality Principle and General Results of Ekeland and Caristi Types without Lower Semicontinuity Assumptions in Cone Uniform Spaces with Generalized Pseudodistances

Kazimierz Włodarczyk and Robert Plebaniak

Department of Nonlinear Analysis, Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238 Łódź, Poland

Received 31 December 2009; Accepted 8 March 2010

Academic Editor: Tomonari Suzuki

Copyright © 2010 Kazimierz Włodarczyk and Robert Plebaniak. 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

Our aim is twofold: first, we want to introduce a partial quasiordering in cone uniform spaces with generalized pseudodistances for giving the general maximality principle in these spaces. Second, we want to show how this maximality principle can be used to obtain new and general results of Ekeland and Caristi types without lower semicontinuity assumptions, which was not done in the previous publications on this subject.