Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
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MULTI-VALUED HICKS CONTRACTIONS IN 𝑏-MENGER SPACES

  • Youssef Achtoun (Department of Mathematics Computing and Physical Sciences, Normal Higher School, Abdelmalek Essaadi University) ;
  • Mohammed Sefian Lamarti (Department of Mathematics Computing and Physical Sciences, Normal Higher School, Abdelmalek Essaadi University) ;
  • Ismail Tahiri (Department of Mathematics Computing and Physical Sciences, Normal Higher School, Abdelmalek Essaadi University)
  • Received : 2023.08.27
  • Accepted : 2024.03.13
  • Published : 2024.06.15
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Abstract

In this work, we will generalize the notion of multivalued (ν, 𝒞)-contraction mapping in 𝑏-Menger spaces and we shall give a new fixed point result of this type of mappings. As a consequence of our main result, we obtained the corresponding fixed point theorem in fuzzy 𝑏-metric spaces. Also, an example will be given to illustrate the main theorem in ordinary 𝑏-metric spaces.

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References

  1. O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht, 2001.
  2. T.L. Hicks, Fixed point theory in probabilistic metric spaces, Zb.Rad. Prirod. Mat. Fak. Ser. Mat., 13 (1983), 63-72.
  3. O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 326-334.
  4. A. Mbarki and J. Hlal, Weakly-H contraction fixed point theorem in 𝑏-Menger spaces, Int. J. Appl. Math., 35(2) (2022), 225-232; doi: 10.12732/ijam.v35i2.2.
  5. A. Mbarki and R. Oubrahim, Probabilistic 𝑏-metric spaces and nonlinear contractions, Fixed Point Theory Appl., 2017 (2017), 15-29. https://doi.org/10.1186/s13663-017-0609-9
  6. A. Mbarki and R. Oubrahim, Common fixed point theorem in 𝑏-Menger spaces with a fully convex structure, Int. J. Appl. Math., 32(2) (2019), 219-238; doi: 10.12732/ijam.v32i5.1.
  7. A. Mbarki and R. Oubrahim, Fixed point theorem satisfying cyclical conditions in 𝑏-Menger spaces, Moroccan J. Pure. Appl. Anal., 5(1) (2019), 31-36. https://doi.org/10.2478/mjpaa-2019-0003
  8. D. Mihet, Multi-valued generalization of probabilistic contractions, J. Math. Anal. Appl., 304 (2005), 464-472. https://doi.org/10.1016/j.jmaa.2004.09.034
  9. S. Nadaban, Fuzzy 𝑏-metric Spaces, Int. J. Comput. Commun., 11 (2016), 273-281. https://doi.org/10.15837/ijccc.2016.2.2443
  10. E. Pap, O. Hadzic and R. Mesiar, A fixed point theorem in probabilistic metric spaces and applications in fuzzy set theory, J. Math. Anal. Appl., 202 (1996), 433-449. https://doi.org/10.1006/jmaa.1996.0325
  11. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, New York, 1983.