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Coupled Fixed Point Theorems for ( )-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications

Author

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  • Manish Jain
  • Neetu Gupta
  • Sanjay Kumar

Abstract

The object of this paper is to establish the existence and uniqueness of coupled fixed points under a ( , )-contractive condition for mixed monotone operators in the setup of partially ordered metric spaces. Presented work generalizes the recent results of Berinde (2011, 2012) and weakens the contractive conditions involved in the well-known results of Bhaskar and Lakshmikantham (2006), and Luong and Thuan (2011). The effectiveness of our work is validated with the help of a suitable example. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.

Suggested Citation

  • Manish Jain & Neetu Gupta & Sanjay Kumar, 2014. "Coupled Fixed Point Theorems for ( )-Contractive Mixed Monotone Mappings in Partially Ordered Metric Spaces and Applications," International Journal of Analysis, Hindawi, vol. 2014, pages 1-9, March.
    • Handle: RePEc:hin:ijanal:586096
    DOI: 10.1155/2014/586096
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    References listed on IDEAS

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    1. A. Branciari, 2002. "A fixed point theorem for mappings satisfying a general contractive condition of integral type," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 29, pages 1-6, January.
    2. Manish Jain & Kenan Tas & Sanjay Kumar & Neetu Gupta, 2012. "Coupled Fixed Point Theorems for a Pair of Weakly Compatible Maps along with CLRg Property in Fuzzy Metric Spaces," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-13, August.
    3. Tomonari Suzuki, 2007. "Meir-Keeler Contractions of Integral Type Are Still Meir-Keeler Contractions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-6, December.
    4. Manish Jain & Kenan Taş, 2013. "A Unique Coupled Common Fixed Point Theorem for Symmetric -Contractive Mappings in Ordered -Metric Spaces with Applications," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-13, December.
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