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On Modified R-Functions and Modified R-Contractions with Fixed Point Results and Applications

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Abstract

In recent times, fixed point theory has undergone a great development, especially through the use of new auxiliary functions and also by weakening the axioms that characterize a metric space. In this work, in the setting of b-metric spaces, the notions of a modified R-function and an \(R_s\)-contraction are introduced and some new fixed point results for such contractions involving modified R-functions are established. Also, we give some example for supporting our results. Finally, we prove some application by using the main results.

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Acknowledgements

The second author would like to thank the Thailand Research Fund and Office of the Higher Education Commission under Grant No. MRG6180283 for financial support during the preparation of this manuscript. A.F. Roldán López de Hierro has been partially supported by Junta de Andalucía by project FQM-268 of the Andalusian CICYE, and also by Project TIN2017-89517-P of Ministerio de Economía, Industria y Competitividad.

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Authors and Affiliations

  1. Faculty of Sports and Health Science, Thailand National Sports University Suphanburi Campus, Suphan Buri, 72000, Thailand

    Oratai Yamaod

  2. Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, Pathumthani, 12120, Thailand

    Wutiphol Sintunavarat

  3. Department of Mathematics Education, Faculty of Education Sciences, University of Granada, Granada, Spain

    Antonio Francisco Roldán López de Hierro

Authors
  1. Oratai Yamaod
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  2. Wutiphol Sintunavarat
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  3. Antonio Francisco Roldán López de Hierro
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Correspondence to Wutiphol Sintunavarat.

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Communicated by: Fuad Kittaneh.

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Yamaod, O., Sintunavarat, W. & Roldán López de Hierro, A.F. On Modified R-Functions and Modified R-Contractions with Fixed Point Results and Applications. Bull. Malays. Math. Sci. Soc. 43, 2713–2732 (2020). https://doi.org/10.1007/s40840-019-00832-7

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  • DOI: https://doi.org/10.1007/s40840-019-00832-7

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