On fixed point theorems of monotone functions in Ordered metric spaces

Abstract

The purpose of this paper is to establish some coincidence point results for f-nondecreasing self-mapping satisfying certain rational type contractions in the frame work of a metric space endowed with partial order. Some consequences of the main result are given by involving integral type contractions in the space. Some examples are illustrated to support our results. Further, as an application we prove the existence of a unique solution of integral equation by the method of upper and lower solutions.

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Acknowledgements

The authors thank the editor and anonymous referees for their valuable suggestion which improved the content of the paper.

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All authors contributed equally to the writing of this paper. All authors read and approved the final manuscript.

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Correspondence to K. Kalyani.

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Communicated by Samy Ponnusamy.

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Kalyani, K., Seshagiri Rao, N. & Mitiku, B. On fixed point theorems of monotone functions in Ordered metric spaces. J Anal (2021). https://doi.org/10.1007/s41478-021-00308-7

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Keywords

  • Partially ordered metric space
  • rational contractions
  • compatible and weakly compatible mappings
  • monotone f-nondecreasing

Mathematics Subject Classification

  • 41A50
  • 47H10
  • 26A42
  • 46T99