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Báo cáo hóa học: "Research Article Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity"

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 Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 169837 16 pages doi 10.1155 2010 169837 Research Article Fixed Points of Single- and Set-Valued Mappings in Uniformly Convex Metric Spaces with No Metric Convexity Rafa Espinola 1 Aurora Fernandez-Leon 1 and BoZena Piatek2 1 Departamento de Analisis Matemứtico Universidad de Sevilla P.O. Box 1160 41080 Sevilla Spain 2 Institute of Mathematics Silesian University of Technology 44-100 Gliwice Poland Correspondence should be addressed to Rafa Espinola espinola@us.es Received 20 April 2009 Accepted 28 May 2009 Academic Editor Mohamed A. Khamsi Copyright 2010 Rafa Espinola 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. We study the existence of fixed points and convergence of iterates for asymptotic pointwise contractions in uniformly convex metric spaces. We also study the existence of fixed points for setvalued nonexpansive mappings in the same class of spaces. Our results do not assume convexity of the metric which makes a big difference when studying the existence of fixed points for set-valued mappings. 1. Introduction This paper is motivated by the recent paper 1 . In 1 the authors study different questions related to fixed points of asymptotic pointwise contractive nonexpansive mappings in CAT 0 spaces. CAT 0 spaces are studied in 1 as a very significant example within the class of uniformly convex metric spaces the reader can consult 2 for details on CAT 0 spaces . In our present paper we propose to consider similar questions on uniformly convex metric spaces under the mildest additional conditions we may impose. More precisely we will work with uniformly convex metric spaces with either a monotone modulus of convexity in the sense first given in 3 or a lower semicontinuous from the right modulus of .