Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010, Article ID 190606, 16 pages doi: Research Article Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems Wei-Shih Du Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 802, Taiwan Correspondence should be addressed to Wei-Shih Du, wsdu@ Received 19 April 2010; Revised 8 June 2010; Accepted 5 July 2010 Academic Editor: Juan J. Nieto Copyright q 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. We establish some new. | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 190606 16 pages doi 2010 190606 Research Article Nonlinear Contractive Conditions for Coupled Cone Fixed Point Theorems Wei-Shih Du Department of Mathematics National Kaohsiung Normal University Kaohsiung 802 Taiwan Correspondence should be addressed to Wei-Shih Du wsdu@ Received 19 April 2010 Revised 8 June 2010 Accepted 5 July 2010 Academic Editor Juan J. Nieto 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. We establish some new coupled fixed point theorems for various types of nonlinear contractive maps in the setting of quasiordered cone metric spaces which not only obtain several coupled fixed point theorems announced by many authors but also generalize them under weaker assumptions. 1. Introduction The existence of fixed point in partially ordered sets has been studied and investigated recently in 1-13 and references therein. Since the various contractive conditions are important in metric fixed point theory there is a trend to weaken the requirement on contractions. Nieto and Rodriguez-Lopez in 8 10 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 by applying fixed point theorems are presented in 2 6 9 11 12 . In 3 13 the authors proved some fixed point theorems for a mixed monotone mapping in a metric space endowed with partial order and applied their results to problems of existence and uniqueness of solutions for some boundary value problems. In 2006 Bhaskar and Lakshmikantham 2 first proved the following interesting coupled fixed point theorem in partially ordered metric spaces. Theorem BL Bhaskar
