tailieunhanh - Báo cáo hóa học: " Research Article Best Proximity Pairs Theorems for Continuous Set-Valued Maps"

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 Theorems for Continuous Set-Valued Maps | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 607926 9 pages doi 2008 607926 Research Article Best Proximity Pairs Theorems for Continuous Set-Valued Maps 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 15 July 2008 Accepted 16 September 2008 Recommended by Nan-jing Huang A best proximity pair for a set-valued map F A B with respect to a set-valued map G A A is defined and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application we derive a coincidence point theorem. 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 A and B be nonempty subsets of M. Let d A B inf d a b a e A b e B and Prox A B a b e A X B d a b d A Bf . A is said to be approximately compact if for each y e M and each sequence xn in A satisfying the condition d xn y d y A there is a subsequence of xn converging to an element of A. Let B0 b e B d a b d A B for some a e A A0 a e A d a b d A B for some b e B . Let G A A and F A B be set-valued maps. G xo F xo is called a best proximity pair for F with respect to G if d G x0 F x0 d A B . Best proximity pair theorems analyze the conditions under which the problem of minimizing the real-valued function x d G x F x has a solution. In the .