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báo cáo hóa học:" Research Article On Fixed Point Theorems for Multivalued Contractions"

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 On Fixed Point Theorems for Multivalued Contractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 870980 18 pages doi 10.1155 2010 870980 Research Article On Fixed Point Theorems for Multivalued Contractions Zeqing Liu 1 Wei Sun 1 Shin Min Kang 2 and Jeong Sheok Ume3 1 Department of Mathematics Liaoning Normal University Dalian Liaoning 116029 China 2 Department of Mathematics and RINS Gyeongsang National University Jinju 660-701 Republic of Korea 3 Department of Applied Mathematics Changwon National University Changwon 641-773 Republic of Korea Correspondence should be addressed to Shin Min Kang smkang@gnu.ac.kr Received 13 August 2010 Accepted 15 November 2010 Academic Editor N. J. Huang Copyright 2010 Zeqing Liu 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. Three concepts of multivalued contractions in complete metric spaces are introduced and the conditions guaranteeing the existence of fixed points for the multivalued contractions are established. The results obtained in this paper extend genuinely a few fixed point theorems due to Ciric 2009 Feng and Liu 2006 and Klim and Wardowski 2007 . Five examples are given to explain our results. 1. Introduction and Preliminaries Let X d be a metric space and let CL X CB X and C X denote the families of all nonempty closed all nonempty closed and bounded and all nonempty compact subsets of X respectively. For any U V e CL X and x e X let d x U inf d x y y e U and H U V max sup d u V sup d v U if the maximum exists 1.1 x otherwise. Such a mapping H is called a generalized Hausdorff metric in CL X induced by d. Throughout this paper we assume that R R and N denote the sets of all real numbers nonnegative real numbers and positive integers respectively. 2 Fixed Point Theory and Applications The existence of fixed points for various multivalued contractive .