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 for Generalized Contractive Multimaps in Metric Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 432130 16 pages doi 2009 432130 Research Article Fixed Point Results for Generalized Contractive Multimaps in Metric Spaces 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 14884 Jeddah 21434 Saudi Arabia Correspondence should be addressed to Abdul Latif latifmath@ Received 17 May 2009 Accepted 10 August 2009 Recommended by Mohamed A. Khamsi The concept of generalized contractive multimaps in the setting of metric spaces is introduced and the existence of fixed points for such maps is guaranteed under certain conditions. Consequently our results either generalize or improve a number of fixed point results including the corresponding recent fixed point results of Ciric 2008 Latif-Albar 2008 Klim-Wardowski 2007 and Feng-Liu 2006 . Examples are also given. 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 and Preliminaries Let X d be a metric space 2X a collection of nonempty subsets of X CB X a collection of nonempty closed bounded subsets of X Cl X a collection of nonempty closed subsets of X K X a collection of nonempty compact subsets of X and H the Hausdorff metric induced by d. Then for any A B e CB X H A B max supd x B supd y A xeA yeB where d x BJ infyeBd x y . An element x e X is called a fixed point of a multivalued map T X 2X 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 xn-1 for all n 1. A map f X R is called lower semicontinuous if for any sequence xn c X with xn x e X it implies that f x lim infn mf xn . 2 Fixed Point Theory
