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Báo cáo hóa học: " Research Article Existence and Data Dependence of Fixed Points and Strict Fixed Points for "

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 Existence and Data Dependence of Fixed Points and Strict Fixed Points for | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 34248 8 pages doi 10.1155 2007 34248 Research Article Existence and Data Dependence of Fixed Points and Strict Fixed Points for Contractive-Type Multivalued Operators Cristian Chifu and Gabriela Petruẹel Received 21 October 2006 Revised 1 December 2006 Accepted 2 December 2006 Recommended by Simeon Reich The purpose of this paper is to present several existence and data dependence results of the fixed points of some multivalued generalized contractions in complete metric spaces. As for application a continuation result is given. Copyright 2007 C. Chifu and G. Petrusel. 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 the standard notations and terminologies in nonlinear analysis see 14 15 are used. For the convenience of the reader we recall some of them. Let X d be a metric space. By B x0 r we denote the closed ball centered in x0 e X with radius r 0. Also we will use the following symbols P X Y c X I Y is nonempty Pcl X Y e P X I Y is closed I 1 c 1.1 Pb X Y e P X I Y is bounded Pb d X Pcl X n Pb X . Let A and B be nonempty subsets of the metric space X d . The gap between these sets is D A B inf d a b I a e A b e B . 1.2 In particular D x0 B D x0 B where x0 e X is called the distance from the point x0 to the set B. 2 Fixed Point Theory and Applications The Pompeiu-Hausdorff generalized distance between the nonempty closed subsets A and B of the metric space X d is defined by the following formula H A B max sup inf d a b supinf d a b . 1.3 aeAbeB beBaeA If A B e Pb cl X then one denotes S A B sup d a b I a e A b e B . 1.4 The symbol T X P Y denotes a set-valued operator from X to Y. We will denote by Graph T x y e X X Y I y e T x the graph of T. Recall that the set-valued .