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Báo cáo hóa học: "Coupled coincidence points for monotone operators in partially ordered metric spaces"

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 www.fixedpointtheoryandapplications.eom 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@hotmail.com Department of Mathematics King Abdulaziz University P.O. 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 .