Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces |
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| Authors: | V. Lakshmikantham,Ljubomir &#x iri&#x |
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| Affiliation: | aDepartment of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA;bFaculty of Mechanical Engineering, Kraljice Marije 16, 11 000 Belgrade, Serbia |
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| Abstract: | We introduce the concept of a mixed g-monotone mapping and prove coupled coincidence and coupled common fixed point theorems for such nonlinear contractive mappings in partially ordered complete metric spaces. Presented theorems are generalizations of the recent fixed point theorems due to Bhaskar and Lakshmikantham [T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379–1393] and include several recent developments. |
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| Keywords: | Coupled fixed point Coupled coincidence Coupled common fixed point Partially ordered set Mixed monotone mapping |
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