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Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction

Author

Listed:
  • Poom Kumam
  • Fayyaz Rouzkard
  • Mohammad Imdad
  • Dhananjay Gopal

Abstract

Ran and Reurings (2004) established an interesting analogue of Banach Contraction Principle in a complete metric space equipped with a partial ordering and also utilized the same oneto discuss the existence of solutions to matrix equations. Motivated by this paper, we prove results on coincidence points for a pair of weakly increasing mappings satisfying a nonlinear contraction condition described by a rational expression on an ordered complete metric space. The uniqueness of common fixed point is also discussed. Some examples are furnished to demonstrate the validity of the hypotheses of our results. As an application, we derive an existence theorem for the solution of an integral equation.

Suggested Citation

  • Poom Kumam & Fayyaz Rouzkard & Mohammad Imdad & Dhananjay Gopal, 2013. "Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-9, August.
    • Handle: RePEc:hin:jnlaaa:206515
    DOI: 10.1155/2013/206515
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    Cited by:

    1. Seher Sultan Yeşilkaya & Cafer Aydın, 2020. "Fixed Point Results of Expansive Mappings in Metric Spaces," Mathematics, MDPI, vol. 8(10), pages 1-10, October.

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