Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Maximality Principle and General Results of Ekeland and Caristi Types without Lower | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 175453 35 pages doi 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 Wtodarczyk and Robert Plebaniak Department of Nonlinear Analysis Faculty of Mathematics and Computer Science University of Lodz Banacha 22 9o-238 Lodi. Poland Correspondence should be addressed to Kazimierz Wlodarczyk wlkzxa@ Received 31 December 2009 Accepted 8 March 2010 Academic Editor Tomonari Suzuki Copyright 2010 K. Wlodarczyk and R. 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. 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. 1. Introduction The famous Banach contraction principle 1 fundamental in fixed point theory has been extended in many different directions. Among these extensions Caristi s fixed point theorem 2 concerning dissipative maps with lower semicontinuous entropies equivalent to celebrated Ekeland s variational principle 3 providing approximate solutions of nonconvex minimization problems concerning lower semicontinuous maps may be the most valuable one. These results are very useful simple and important tools for investigating various problems in nonlinear analysis mathematical programming control theory abstract economy global analysis and others. They have many .
