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Báo cáo toán học: " Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity"

Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity | Fixed Point Theory and Applications SpringerOpen0 This Provisional PDF corresponds to the article as it appeared upon acceptance. Fully formatted PDF and full text HTML versions will be made available soon. Weak compactness and the Eisenfeld-Lakshmikantham measure of nonconvexity Fixed Point Theory and Applications 2012 2012 5 doi 10.1186 1687-1812-2012-5 Isabel Marrero imarrero@ull.es ISSN 1687-1812 Article type Research Submission date 20 September 2011 Acceptance date 16 January 2012 Publication date 16 January 2012 Article URL http www.fixedpointtheoryandapplications.com content 2012 1 5 This peer-reviewed article was published immediately upon acceptance. It can be downloaded printed and distributed freely for any purposes see copyright notice below . For information about publishing your research in Fixed Point Theory and Applications go to http www.fixedpointtheoryandapplications.com authors instructions For information about other SpringerOpen publications go to http www.springeropen.com 2012 Marrero licensee Springer. This is an open access article distributed under the terms of the Creative Commons Attribution License http creativecommons.org licenses by 2.0 which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. Weak compactness and the Eisenfeld Lakshmikantham measure of nonconvexity Isabel Marrero Departamento de Analisis Matemático Universidad de La Laguna 38271 La Laguna Tenerife Spain Email address imarrero@ull.es Dedicated to the memory of my mother Abstract In this article weakly compact subsets of real Banach spaces are characterized in terms of the Cantor property for the Eisenfeld-Lakshmikantham measure of nonconvexity. This characterization is applied to prove the existence of fixed points for condensing maps nonexpansive maps and isometries without convexity requirements on their domain. Mathematics Subject Classification 2010 Primary 47H10 Secondary 46B20 47H08 47H09. Keywords