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

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.

Keywords

• Generalized b-Menger Space
• Weak Hick Contraction
• Fixed Poin

References

1. [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. [2] O. Hadˇzi´c, A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) T. 20 ,(1979), 107-112.
3. [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. [4] O. Hadˇzi´c, E. Pap, Fixed point theory in probabilistic metric spaces, Kluwer Academic Publishers, Dordrecht (2001).
5. [5] T.L. Hicks, Fixed point theory in PM spaces, Rev. Resh. Novi. Sad., 13, (1983) 63-72.
6. [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. [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. [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. [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. [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. [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. [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. [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. [14] D. Mihet¸, Weak-Hicks contractions, Fixed Point Theory, 6, No 1, (2005), 71-78.
15. [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.