tailieunhanh - Báo cáo hóa học: "Research Article Fixed Points of Generalized Contractive 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 Fixed Points of Generalized Contractive Maps | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 487161 9 pages doi 2009 487161 Research Article Fixed Points of Generalized Contractive Maps Abdul Latif1 and Afrah A. N. Abdou2 1 Department of Mathematics King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia 2 Girls College of Education King Abdulaziz University . Box 55002 Jeddah Saudi Arabia Correspondence should be addressed to Abdul Latif latifmath@ Received 13 October 2008 Accepted 27 January 2009 Recommended by Hichem Ben-El-Mechaiekh We prove some results on the existence of fixed points for multivalued generalized -contractive maps not involving the extended Hausdorff metric. Consequently several known fixed point results are either generalized or improved. Copyright 2009 A. Latif and A. A. N. Abdou. 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 Throughout this paper unless otherwise specified X is a metric space with metric d. Let 2X C X and CB X denote the collection of nonempty subsets of X nonempty closed subsets of X and nonempty closed bounded subsets of X respectively. Let H be the Hausdorff metric on CB X that is H A B max supd x B supd y A A B e CB X . xeA yeB A multivalued map T X CB X is called i contraction 1 if for a fixed constant h e 0 1 and for each x y e X H T x T y hd x y ii generalized contraction 2 if for any x y e X H T x T y k d x yy d x yj 2 Fixed Point Theory and Applications where k is a function from 0 to to 0 1 with limsupr t k r 1 for every t e 0 to iii contractive 3 if there exist constants b h e 0 1 h b such that for any x e X there is y e IX satisfying d y T y hd x y where IX y e T x bd x y d x T x iv generalized contractive 4 if there exist b e 0 1 such that for any x e X there is y e ix satisfying d y T y k