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Báo cáo hóa học: " Research Article Fixed Points of Multivalued Maps in Modular Function 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 Fixed Points of Multivalued Maps in Modular Function Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 786357 12 pages doi 10.1155 2009 786357 Research Article Fixed Points of Multivalued Maps in Modular Function Spaces Marwan A. Kutbi and Abdul Latif Department of Mathematics King Abdulaziz University P. O. Box 80203 Jeddah 21589 Saudi Arabia Correspondence should be addressed to Abdul Latif latifmath@yahoo.com Received 7 February 2009 Accepted 14 April 2009 Recommended by Jerzy Jezierski The purpose of this paper is to study the existence of fixed points for contractive-type and nonexpansive-type multivalued maps in the setting of modular function spaces. We also discuss the concept of w-modular function and prove fixed point results for weakly-modular contractive maps in modular function spaces. These results extend several similar results proved in metric and Banach spaces settings. Copyright 2009 M. A. Kutbi and A. Latif. 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. 1. Introduction and Preliminaries The well-known Banach fixed point theorem on complete metric spaces specifically each contraction self-map of a complete metric space has a unique fixed point has been extended and generalized in different directions. For example see Edelstein 1 2 Kasahara 3 Rhoades 4 Siddiq and Ansari 5 and others. One of its generalizations is for nonexpansive single-valued maps on certain subsets of a Banach space. Indeed these fixed points are not necessarily unique. See for example Browder 6-8 and Kirk 9 . Fixed point theorems for contractive and nonexpansive multivalued maps have also been established by several authors. Let H denote the Hausdorff metric on the space of all bounded nonempty subsets of a metric space X d . A multivalued map J X 2X where 2X denotes the collection of all nonempty subsets of X with bounded .