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báo cáo hóa học:" Research Article Fixed Point Results in Quasimetric Spaces Abdul Latif and Saleh A. Al-Mezel"

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 Point Results in Quasimetric Spaces Abdul Latif and Saleh A. Al-Mezel | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 1788306 8 pages doi 10.1155 2011 178306 Research Article Fixed Point Results in Quasimetric Spaces Abdul Latif and Saleh A. Al-Mezel 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 21 August 2010 Accepted 5 October 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 A. Latif and S. A. Al-Mezel. 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. In the setting of quasimetric spaces we prove some new results on the existence of fixed points for contractive type maps with respect to O-function. Our results either improve or generalize many known results in the literature. 1. Introduction and Preliminaries Let X be a metric space with metric d. We use S X to denote the collection of all nonempty subsets of X Cl X for the collection of all nonempty closed subsets of X CB X for the collection of all nonempty closed bounded subsets of X and H for the Hausdorff metric on CBJXJ that is H A B maxịsupd a B supd b A ị A B e CB X 1.1 where d a B inf d a b b e B is the distance from the point a to the subset B. For a multivalued map T X CB X we say a T is contraction 1 if there exists a constant A e 0 1 such that for all x y e X H T x T yỴ Xd x y 1.2 b T is weakly contractive 2 if there exist constants h b e 0 1 h b such that for any x e X there is y e Ibx satisfying d y T yy hd x y 1.3 where ix y e T x bd x yj d x T x . 2 Fixed Point Theory and Applications A point x e X is called a fixed point of a multivalued map T X S X if x e T x . We denote Fix T x e X x e T x . A sequence xn in X is called an orbit of T at x0 e X if xn e T x -1 for all integer n 1. A real valued function f on X is called lower .