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Báo cáo hóa học: " Coupled coincidences for multi-valued contractions in partially ordered metric spaces"

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Coupled coincidences for multi-valued contractions in partially ordered metric spaces | Hussain and Alotaibi Fixed Point Theory and Applications 2011 2011 82 http www.fixedpointtheoryandapplications.eom content 2011 1 82 Fixed Point Theory and Applications a SpringerOpen Journal RESEARCH Open Access Coupled coincidences for multi-valued contractions in partially ordered metric spaces N Hussain and A Alotaibi Correspondence aalotaibi@kau. edu.sa Department of Mathematics King Abdulaziz University P.O. Box 80203 Jeddah 21589 Saudi Arabia Springer Abstract In this article we study the existence of coupled coincidence points for multi-valued nonlinear contractions in partially ordered metric spaces. We do it from two different approaches the first is A-symmetric property recently studied in Samet and Vetro Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces Nonlinear Anal. 74 4260-4268 2011 and second one is mixed g-monotone property studied by Lakshmikantham and Ciric Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces Nonlinear Anal. 70 4341-4349 2009 . The theorems presented extend certain results due to Ciric Multi-valued nonlinear contraction mappings Nonlinear Anal. 71 2716-2723 2009 Samet and Vetro Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces Nonlinear Anal. 74 4260-4268 2011 and many others. We support the results by establishing an illustrative example. 2000 MSC primary 06F30 46B20 47E10. Keywords coupled coincidence points partially ordered metric spaces compatible maps multi-valued nonlinear contraction mappings 1. Introduction and preliminaries Let X d be a metric space. We denote by CB X the collection of non-empty closed bounded subsets of X. For A B e CB X and x e X suppose that D x A inf d x a and H A B max sup D a B sup D b A . Such a mapping H is called a Hausdorff metric on CB X induced by d. Definition 1.1. An element x e X is said to be a fixed point of a multi-valued .