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Fixed Points for ψ‐Graphic Contractions with Application to Integral Equations

Author

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  • N. Hussain
  • S. Al-Mezel
  • P. Salimi

Abstract

The aim of this paper is to define modified weak α‐ψ‐contractive mappings and to establish fixed point results for such mappings defined on partial metric spaces using the notion of triangular α‐admissibility. As an application, we prove new fixed point results for graphic weak ψ‐contractive mappings. Moreover, some examples and an application to integral equation are given here to illustrate the usability of the obtained results.

Suggested Citation

  • N. Hussain & S. Al-Mezel & P. Salimi, 2013. "Fixed Points for ψ‐Graphic Contractions with Application to Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:575869
    DOI: 10.1155/2013/575869
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    References listed on IDEAS

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    1. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    2. Ravi P. Agarwal & Nawab Hussain & Mohamed-Aziz Taoudi, 2012. "Fixed Point Theorems in Ordered Banach Spaces and Applications to Nonlinear Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, July.
    3. Nawab Hussain & Zoran Kadelburg & Stojan Radenović & Falleh Al-Solamy, 2012. "Comparison Functions and Fixed Point Results in Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-15, June.
    4. Zorana Golubović & Zoran Kadelburg & Stojan Radenović, 2012. "Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-18, March.
    5. Nawab Hussain & Zoran Kadelburg & Stojan Radenović & Falleh Al-Solamy, 2012. "Comparison Functions and Fixed Point Results in Partial Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    6. Zorana Golubović & Zoran Kadelburg & Stojan Radenović, 2012. "Coupled Coincidence Points of Mappings in Ordered Partial Metric Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
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    Cited by:

    1. N. Hussain & M. A. Kutbi & P. Salimi, 2014. "Fixed Point Theory in α‐Complete Metric Spaces with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).

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