tailieunhanh - Báo cáo hóa học: " Research Article Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Space"

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 Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 804734 8 pages doi 2009 804734 Research Article Some Common Fixed Point Theorems for Weakly Compatible Mappings in Metric Spaces M. A. Ahmed Department of Mathematics Faculty of Science Assiut University Assiut 71516 Egypt Correspondence should be addressed to M. A. Ahmed mahmed68@ Received 23 October 2008 Accepted 18 January 2009 Recommended by William A. Kirk We establish a common fixed point theorem for weakly compatible mappings generalizing a result of Khan and Kubiaczyk 1988 . Also an example is given to support our generalization. We also prove common fixed point theorems for weakly compatible mappings in metric and compact metric spaces. Copyright 2009 M. A. Ahmed. 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 In the last years fixed point theorems have been applied to show the existence and uniqueness of the solutions of differential equations integral equations and many other branches mathematics see . 1-3 . Some common fixed point theorems for weakly commuting compatible ổ-compatible and weakly compatible mappings under different contractive conditions in metric spaces have appeared in 4-15 . Throughout this paper fX d is a metric space. Following 9 16 we define 2X A c X A is nonempty B X A e 2X A is bounded . For all A B e B X we define 6 A B sup ịd a b a e A b e B D A B inf d a b a e A b e Bị H A B inf r 0 Ar D B Br D A 2 Fixed Point Theory and Applications where Ar x e X d x a r for some a e A and Br y e X d y b r for some b e B . If A a for some a e A we denote ô a B D a B and H a B for Ô A B D A B and H A B respectively. Also if B b then one can deduce that Ô A B D A B H A B d a b . It follows immediately from the definition of Ô A B that for every A B C e