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Báo cáo hóa học: " Research Article Common Fixed Points for Multimaps in Metric Spaces"

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 Common Fixed Points for Multimaps in Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 204981 14 pages doi 10.1155 2010 204981 Research Article Common Fixed Points for Multimaps in Metric Spaces Rafa Espinola1 and Nawab Hussain2 1 Departamento de Analisis Matematico Universidad de Sevilla P.O. Box 1160 41080 Sevilla Spain 2 Department of Mathematics King Abdul Aziz University P.O. Box 80203 Jeddah Saudi Arabia Correspondence should be addressed to Rafa Espinola espinola@us.es Received 10 June 2009 Accepted 15 September 2009 Academic Editor Tomonari Suzuki Copyright 2010 R. Espinola and N. Hussain. 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 discuss the existence of common fixed points in uniformly convex metric spaces for singlevalued pointwise asymptotically nonexpansive or nonexpansive mappings and multivalued nonexpansive -nonexpansive or e-semicontinuous maps under different conditions of commutativity. 1. Introduction Fixed point theory for nonexpansive and related mappings has played a fundamental role in many aspects of nonlinear functional analysis for many years. The notion of asymptotic pointwise nonexpansive mapping was introduced and studied in 1 2 . Very recently in 3 techniques developed in 1 2 were applied in metric spaces and CAT 0 spaces where the authors attend to the Bruhat-Tits inequality for CAT 0 spaces in order to obtain such results. In 4 it has been shown that these results hold even for a more general class of uniformly convex metric spaces than CAT 0 spaces. Here we take advantage of this recent progress on asymptotic pointwise nonexpansive mappings and existence of fixed points for multivalued nonexpansive mappings in metric spaces to discuss the existence of common fixed points in either uniformly convex metric spaces or R-trees for this kind of mappings as well as .