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 Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 543154 8 pages doi 2008 543154 Research Article Coincidence Point Best Approximation and Best Proximity Theorems for Condensing 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 University of Shahrekord Shahrekord 88186-34141 Iran 2 Department of Mathematics Razi University Kermanshah 67149 Iran 3 Department of Mathematics National University of Ireland Galway Ireland 4 Department of Mathematical Sciences Florida Institute of Technology Melbourne FL 32901 USA Correspondence should be addressed to A. Amini-Harandi aminih_a@ Received 8 October 2008 Accepted 9 December 2008 Recommended by William A. Kirk In hyperconvex metric spaces we first present a coincidence point theorem for condensing setvalued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application we derive a coincidence point theorem for nonself-condensing set-valued maps. 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 The best approximation problem in a hyperconvex metric space consists of finding conditions for given set-valued mappings F and G and a set X such that there is a point x0 6 X satisfying d G x0 F x0 d x F x0 for X e X. When G I the identity mapping and when the set X is compact best approximation theorems for mappings in hyperconvex metric spaces are given for the single-valued case in 1-4 for the set-valued case in 1 3 5-9 . Some results for condensing set-valued maps were given in 2 . Given subsets A B set-valued mappings F A B and G A A the best proximity problem .
