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 Coupled Coincidence Point and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces with w-Distance | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 134897 11 pages doi 2010 134897 Research Article Coupled Coincidence Point and Coupled Common Fixed Point Theorems in Partially Ordered Metric Spaces with w-Distance Mujahid Abbas 1 Dejan Ilic 2 and Muhammad Ali Khan1 1 Department of Mathematics Lahore University of Management Sciences 54792 Lahore Pakistan 2 Department of Mathematics Faculty of Sciences and Mathematics University of Nis ViSegradska 33 18000 Nis Serbia Correspondence should be addressed to Dejan Ilic ilicde@ Received 7 April 2010 Accepted 18 October 2010 Academic Editor Hichem Ben-El-Mechaiekh Copyright 2010 Mujahid Abbas 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. We introduce the concept of a w-compatible mapping to obtain a coupled coincidence point and a coupled point of coincidence for nonlinear contractive mappings in partially ordered metric spaces equipped with w-distances. Related coupled common fixed point theorems for such mappings are also proved. Our results generalize extend and unify several well-known comparable results in the literature. 1. Introduction and Preliminaries In 1996 Kada et al. 1 introduced the notion of -distance. They elaborated with the help of examples that the concept of w-distance is general than that of metric on a nonempty set. They also proved a generalization of Caristi fixed point theorem employing the definition of w-distance on a complete metric space. Recently Ilic and Rakocevic 2 obtained fixed point and common fixed point theorems in terms of w-distance on complete metric spaces see also 3-9 . Definition . Let X d be a metric space. A mapping p X X X 0 to is called a w-distance on X if the following are satisfied w1 p x z p x y p y z for all x y z e X w2 for any x e X p x X 0 .
