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On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces

Year 2025, Volume: 13 Issue: 2, 300 - 304, 31.10.2025

Abstract

This paper investigates the existence of fixed points for weak Hicks contractions in generalized b-Menger spaces. An example is provided to illustrate the validity of the results obtained.

References

  • [1] Y. Achtoun, S. Radenovi ´ c, I. Tahiri, M. L. Sefian, The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation , Nonlinear Analysis: Modelling and Control, Vol. 29, No. 3, (2024) 1-12.
  • [2] O. Hadˇzi´c, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) T. 20 ,(1979), 107-112.
  • [3] O. Hadˇzi´c, E. Pap, M. Budinccvic, Countable extension of triangular norms and their applications to fixed point theory in probabilistic metric spaces, Kibermetica, 38, 3 (2002) 363-381.
  • [4] O. Hadˇzi´c, E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic Publishers, Dordrecht (2001).
  • [5] T.L. Hicks, Fixed point theory in PM spaces, Rev. Resh. Novi. Sad., 13, (1983) 63-72.
  • [6] A. Mbarki, J. Hlal, Weakly-H contraction fixed point theorem in b-menger spaces, International Journal of Applied Mathematics, 35, No 2 (2022), 225–232.
  • [7] A. Mbarki, R. Oubrahim, Probabilistic b-metric spaces and nonlinear contractions, Fixed Point Theory and Applications, 2017, vol. 2017, no 1, p. 29.
  • [8] A. Mbarki, R. Oubrahim, Fixed point theorems with cyclical contractive conditions in b-Menger spaces, Results in Fixed Point Theory and Applications, 2018, (2018); doi: 10.30697/rfpta-2018-005.
  • [9] A. Mbarki, R. Oubrahim, Common fixed point theorems in b-Menger spaces, In: Recent Advances in Intuitionistic Fuzzy Logic Systems. Studies in Fuzziness and Soft Computing, Springer, (2019), 283-289.
  • [10] A. Mbarki, R. Oubrahim, Common fixed point theorem in b-Menger spaces with a fully convex structure, Int. J. Appl. Math., 32, No 2, (2019), 219-238; doi: 10.12732/ijam.v32i5.1.
  • [11] A. Mbarki, R. Oubrahim, Fixed point theorem satisfying cyclical conditions in b-Menger spaces, Moroccan J. Pure. Appl. Anal., 5, No 1, (2019), 31-36.
  • [12] A. Mbarki, R. Oubrahim, Probabilistic j-contraction in b-Menger spaces with fully convex structure, Int. J. Appl. Math., 33, No 4 (2020), 621-633.
  • [13] A. Mbarki, R. Oubrahim, Some properties of convexity structure and applications in b-Menger spaces, In : Mathematical and Computational Methods for Modelling, Approximation and Simulation. Cham : Springer International Publishing, 2022. p. 181-189.
  • [14] D. Mihet¸, Weak-Hicks contractions, Fixed Point Theory, 6, No 1, (2005), 71-78.
  • [15] R. Oubrahim, R. Naciri, A. Mbarki, Fixed point theorems in generalized b-Menger spaces, Results in Nonlinear Analysis, 7 (2024) No. 1, 35-43. [16] B. Schweizer, H. Sherwood and R.M. Tradif, Contractions on probabilistic metric spaces: examples and counterexamples, Stochastica., XII, 1 (1988), 5-17.

Year 2025, Volume: 13 Issue: 2, 300 - 304, 31.10.2025

Abstract

References

  • [1] Y. Achtoun, S. Radenovi ´ c, I. Tahiri, M. L. Sefian, The nonlinear contraction in probabilistic cone b-metric spaces with application to integral equation , Nonlinear Analysis: Modelling and Control, Vol. 29, No. 3, (2024) 1-12.
  • [2] O. Hadˇzi´c, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) T. 20 ,(1979), 107-112.
  • [3] O. Hadˇzi´c, E. Pap, M. Budinccvic, Countable extension of triangular norms and their applications to fixed point theory in probabilistic metric spaces, Kibermetica, 38, 3 (2002) 363-381.
  • [4] O. Hadˇzi´c, E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic Publishers, Dordrecht (2001).
  • [5] T.L. Hicks, Fixed point theory in PM spaces, Rev. Resh. Novi. Sad., 13, (1983) 63-72.
  • [6] A. Mbarki, J. Hlal, Weakly-H contraction fixed point theorem in b-menger spaces, International Journal of Applied Mathematics, 35, No 2 (2022), 225–232.
  • [7] A. Mbarki, R. Oubrahim, Probabilistic b-metric spaces and nonlinear contractions, Fixed Point Theory and Applications, 2017, vol. 2017, no 1, p. 29.
  • [8] A. Mbarki, R. Oubrahim, Fixed point theorems with cyclical contractive conditions in b-Menger spaces, Results in Fixed Point Theory and Applications, 2018, (2018); doi: 10.30697/rfpta-2018-005.
  • [9] A. Mbarki, R. Oubrahim, Common fixed point theorems in b-Menger spaces, In: Recent Advances in Intuitionistic Fuzzy Logic Systems. Studies in Fuzziness and Soft Computing, Springer, (2019), 283-289.
  • [10] A. Mbarki, R. Oubrahim, Common fixed point theorem in b-Menger spaces with a fully convex structure, Int. J. Appl. Math., 32, No 2, (2019), 219-238; doi: 10.12732/ijam.v32i5.1.
  • [11] A. Mbarki, R. Oubrahim, Fixed point theorem satisfying cyclical conditions in b-Menger spaces, Moroccan J. Pure. Appl. Anal., 5, No 1, (2019), 31-36.
  • [12] A. Mbarki, R. Oubrahim, Probabilistic j-contraction in b-Menger spaces with fully convex structure, Int. J. Appl. Math., 33, No 4 (2020), 621-633.
  • [13] A. Mbarki, R. Oubrahim, Some properties of convexity structure and applications in b-Menger spaces, In : Mathematical and Computational Methods for Modelling, Approximation and Simulation. Cham : Springer International Publishing, 2022. p. 181-189.
  • [14] D. Mihet¸, Weak-Hicks contractions, Fixed Point Theory, 6, No 1, (2005), 71-78.
  • [15] R. Oubrahim, R. Naciri, A. Mbarki, Fixed point theorems in generalized b-Menger spaces, Results in Nonlinear Analysis, 7 (2024) No. 1, 35-43. [16] B. Schweizer, H. Sherwood and R.M. Tradif, Contractions on probabilistic metric spaces: examples and counterexamples, Stochastica., XII, 1 (1988), 5-17.
There are 15 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Research Article
Authors

Abderrahim Mbarkı

Publication Date October 31, 2025
Submission Date November 10, 2024
Acceptance Date December 17, 2024
Published in Issue Year 2025 Volume: 13 Issue: 2

Cite

APA Mbarkı, A. (2025). On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces. Konuralp Journal of Mathematics, 13(2), 300-304.
AMA Mbarkı A. On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces. Konuralp J. Math. October 2025;13(2):300-304.
Chicago Mbarkı, Abderrahim. “On the Existence of Fixed Points for Weak Hicks Contractions in Generalized B-Menger Spaces”. Konuralp Journal of Mathematics 13, no. 2 (October 2025): 300-304.
EndNote Mbarkı A (October 1, 2025) On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces. Konuralp Journal of Mathematics 13 2 300–304.
IEEE A. Mbarkı, “On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces”, Konuralp J. Math., vol. 13, no. 2, pp. 300–304, 2025.
ISNAD Mbarkı, Abderrahim. “On the Existence of Fixed Points for Weak Hicks Contractions in Generalized B-Menger Spaces”. Konuralp Journal of Mathematics 13/2 (October2025), 300-304.
JAMA Mbarkı A. On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces. Konuralp J. Math. 2025;13:300–304.
MLA Mbarkı, Abderrahim. “On the Existence of Fixed Points for Weak Hicks Contractions in Generalized B-Menger Spaces”. Konuralp Journal of Mathematics, vol. 13, no. 2, 2025, pp. 300-4.
Vancouver Mbarkı A. On the Existence of Fixed Points for Weak Hicks Contractions in Generalized b-Menger Spaces. Konuralp J. Math. 2025;13(2):300-4.
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