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 Best Proximity Pairs for Upper Semicontinuous Set-Valued Maps in Hyperconvex Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 648985 5 pages doi 2008 648985 Research Article Best Proximity Pairs for Upper Semicontinuous Set-Valued Maps in Hyperconvex Metric Spaces A. Amini-Harandi 1 A. P. Farajzadeh 2 D. O Regan 3 and R. P. Agarwal4 1 Department of Mathematics Faculty of Basic Sciences University of Shahrekord Shahrekord 88186-34141 Iran 2 Department of Mathematics School of Science Razi University Kermanshah 67149 Iran 3 Department of Mathematics College of Arts Social Sciences and Celtic Studies National University of Ireland Galway Ireland 4 Department of Mathematical Sciences College of Science Florida Institute of Technology Melbourne FL 32901 USA Correspondence should be addressed to A. Amini-Harandi aminih_a@ Received 14 July 2008 Accepted 27 October 2008 Recommended by Nan-jing Huang A best proximity pair for a set-valued map F A B with respect to a map g A A is defined and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism are proved in hyperconvex metric spaces. Copyright 2008 A. Amini-Harandi 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. 1. Introduction and preliminaries Let M d be a metric space and let Aand B be nonempty subsets of M. Let g A A and let F A B be a set-valued map. Now g a F a is called a best proximity pair for F with respect to g if d g a F a d A B where d A B inf d a b a e A b e B . Best proximity pair theorems establish conditions under which the problem of minimizing the real-valued function x d g x F x has a solution. In the setting of normed linear spaces the best proximity pair problem has been studied by many authors for g I see 1-5 . Very recently Al-Thagafi and Shahzad 1 proved some existence theorems for a .
