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: Coupled coincidence points for monotone operators in partially ordered metric spaces | Alotaibi and Alsulami Fixed Point Theory and Applications 2011 2011 44 http content 2011 1 44 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Coupled coincidence points for monotone operators in partially ordered metric spaces Abdullah Alotaibi and Saud M Alsulami Correspondence mathker11@ Department of Mathematics King Abdulaziz University . Box 80203 Jeddah 21589 Saudi Arabia Springer Abstract Using the notion of compatible mappings in the setting of a partially ordered metric space we prove the existence and uniqueness of coupled coincidence points involving a j -contractive condition for a mappings having the mixed g-monotone property. We illustrate our results with the help of an example. Keywords coupled coincidence point partially ordered metric space mixed g-monotone property 1 Introduction The Banach contraction principle is the most celebrated fixed point theorem. Afterward many authors obtained many important extensions of this principle cf. 1-16 . Recently Bhaskar and Lakshmikantham 5 Nieto and Lopez 12 13 Ran and Reurings 14 and Agarwal et al. 3 presented some new results for contractions in partially ordered metric spaces. Bhaskar and Lakshmikantham 5 noted that their theorem can be used to investigate a large class of problems and have discussed the existence and uniqueness of solution for a periodic boundary value problem. Recently Luong and Thuan 11 presented some coupled fixed point theorems for a mixed monotone mapping in a partially ordered metric space which are generalizations of the results of Bhaskar and Lakshmikantham 5 . In this paper we establish the existence and uniqueness of coupled coincidence point involving a j -contractive condition for mappings having the mixed g-monotone property. We also illustrate our results with the help of an example. 2 Preliminaries A partial order is a binary relation 4 over a set X which is reflexive antisymmetric and .
