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Fixed Point Theory in α‐Complete Metric Spaces with Applications

Author

Listed:
  • N. Hussain
  • M. A. Kutbi
  • P. Salimi

Abstract

The aim of this paper is to introduce new concepts of α‐η‐complete metric space and α‐η‐continuous function and establish fixed point results for modified α‐η‐ψ‐rational contraction mappings in α‐η‐complete metric spaces. As an application, we derive some Suzuki type fixed point theorems and new fixed point theorems for ψ‐graphic‐rational contractions. Moreover, some examples and an application to integral equations are given here to illustrate the usability of the obtained results.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:280817
    DOI: 10.1155/2014/280817
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    References listed on IDEAS

    as
    1. N. Hussain & M. A. Kutbi & P. Salimi, 2013. "Best Proximity Point Results for Modified α‐ψ‐Proximal Rational Contractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(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, John Wiley & Sons, vol. 2012(1).
    3. 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.
    4. Erdal Karapınar & Bessem Samet, 2012. "Generalized α‐ψ Contractive Type Mappings and Related Fixed Point Theorems with Applications," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    5. N. Hussain & S. Al-Mezel & P. Salimi, 2013. "Fixed Points for -Graphic Contractions with Application to Integral Equations," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-11, October.
    6. N. Hussain & M. A. Kutbi & P. Salimi, 2013. "Best Proximity Point Results for Modified - -Proximal Rational Contractions," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, August.
    7. 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).
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