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 Fixed Point Theorems for Nonlinear Contractions Satisfied Mizoguchi-Takahashi’s Condition in Quasiordered Metric Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 876372 9 pages doi 2010 876372 Research Article Coupled Fixed Point Theorems for Nonlinear Contractions Satisfied Mizoguchi-Takahashi s Condition in Quasiordered Metric Spaces Wei-Shih Du Department of Mathematics National Kaohsiung Normal University Kaohsiung 802 Taiwan Correspondence should be addressed to Wei-Shih Du wsdu@ Received 10 November 2009 Revised 5 March 2010 Accepted 14 March 2010 Academic Editor Tomonari Suzuki Copyright 2010 Wei-Shih Du. 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. The main aim of this paper is to study and establish some new coupled fixed point theorems for nonlinear contractive maps that satisfied Mizoguchi-Takahashi s condition in the setting of quasiordered metric spaces or usual metric spaces. 1. Introduction Let X d be a metric space. For each x e X and A c X let d x A infyeA d x y . Denote by N X the class of all nonempty subsets of X and CB X the family of all nonempty closed and bounded subsets of X. A function H CB X X CB X 0 to defined by H A B max supd x A supd x B is said to be the Hausdorff metric on CB X induced by the metric d on X. A point x in X is a fixed point of a map T if Tx x when T X X is a single-valued map or x e Tx when T X N X is a multivalued map . Throughout this paper we denote by N and R the set of positive integers and real numbers respectively. The existence of fixed point in partially ordered sets has been investigated recently in 1-11 and references therein. In 6 8 Nieto and Rodriguez-Lopez used Tarski s theorem to show the existence of solutions for fuzzy equations and fuzzy differential equations respectively. The existence of solutions for matrix equations or ordinary differential equations 2 Fixed Point Theory .
