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Fixed point theorems for ϕ-contraction mappings in probabilistic generalized Menger space

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Abstract

In this paper, we define the concepts of ϕ-contraction in probabilistic generalized Menger space. We prove that ϕ-contraction mappings in probabilistic generalized Menger space have a unique fixed point. Also we prove some fixed point theorems related this concept. Some examples are given to support the obtained results.

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References

  1. S. M. Alsulami, B. S. Choudhury, and P. Das, ϕ-contraction in generalized probabilistic metric spaces, Fixed Point Theory Appl., 2015 (2015), 151.

    Article  MathSciNet  Google Scholar 

  2. B. S. Choudhury and K. P. Das, A new contraction principle in Menger spaces, Acta Math. Sin., 24 (2008), 1379–1386.

    Article  MathSciNet  Google Scholar 

  3. B. C. Dhage, Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc., 84 (1992), 329–336.

    MathSciNet  MATH  Google Scholar 

  4. S. Gahler, 2-metrische Raume undihre topologische Struktur, Math. Nachr., 26 (1963), 115–148.

    Article  MathSciNet  Google Scholar 

  5. K. S. Ha, Y. J. Cho, and A. White, Strictly convex and strictly 2-convex 2-normed spaces, Math. Japon., 33 (1988), 375–384.

    MathSciNet  MATH  Google Scholar 

  6. M. S. Khan, M. Swaleh, and S. Sessa, Fixed points theorems by altering distances between the points, Bull. Aust. Math. Soc., 30 (1984), 1–9.

    Article  MathSciNet  Google Scholar 

  7. K. Menger, Statistical metrics, Proc. Natl. Acad. Sci. U. S. A., 28 (1942), 535–537.

    Article  MathSciNet  Google Scholar 

  8. Z. Mustafa, M. Khandaqji, and W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math. Hung., 48 (2011), 304–319.

    MathSciNet  MATH  Google Scholar 

  9. Z. Mustafa, W. Shatanawi, and M. Bataineh, Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., (2009).

    Google Scholar 

  10. Z. Mustafa and B. Sims, Remarks concerning D-metric spaces, Proceedings of the International Conference on Fixed Point Theory and Applications, 2003, Valencia, Spain.

  11. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289–297.

    MathSciNet  MATH  Google Scholar 

  12. Z. Mustafa, H. Obiedat, and F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008 (2008), 189870.

    Article  MathSciNet  Google Scholar 

  13. A. Roldn, E. Karapnar and P. Kumam, G-Metric spaces in any number of arguments and related fixedpoint theorems, Fixed Point Theory Appl., 2014 (2014), 13.

    Article  Google Scholar 

  14. B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland. New York (1983).

    MATH  Google Scholar 

  15. W. Shatanawi, Coupled fixed point theorems in generalized metric spaces, Hacet. J. Math. Stat., 40 (2011), 441–447.

    MathSciNet  MATH  Google Scholar 

  16. C. Zhou, SH. Wang, L. Ciric, and S. Alsulami, Generalized probabilistic metric spaces and fixed point theorems, Fixed Point Theory Appl., 2014 (2014), 91.

    Article  MathSciNet  Google Scholar 

  17. C. Zhu, Q. Tu, and Z. Wu, Common fixed point theorems for three pairs of self-mappings satisfying the common (E.A) property in Menger probabilistic G-metric spaces, Fixed Point Theory Appl., 2015 (2015), 131.

    Article  MathSciNet  Google Scholar 

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Acknowledgement

The author would like to express this sincere appreciation to the Shahrekord university and the center of excellence for mathematics for financial supports.

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Authors and Affiliations

  1. Department of Pure Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran

    Shahnaz Jafari & Maryam Shams

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  1. Shahnaz Jafari
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  2. Maryam Shams
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Correspondence to Shahnaz Jafari or Maryam Shams.

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Jafari, S., Shams, M. Fixed point theorems for ϕ-contraction mappings in probabilistic generalized Menger space. Indian J Pure Appl Math 51, 519–532 (2020). https://doi.org/10.1007/s13226-020-0414-8

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  • DOI: https://doi.org/10.1007/s13226-020-0414-8

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