Fixed Point Theorems on Ordered Metric Spaces through a Rational Contraction

Poom Kumam, Fayyaz Rouzkard, Mohammad Imdad and Dhananjay Gopal

Abstract and Applied Analysis, 2013, vol. 2013, 1-9

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:206515

DOI: 10.1155/2013/206515

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