Fixed point theorems in generalized b-Menger spaces

Abstract views: 210 / PDF downloads: 203


  • Rachid OUBRAHIM
  • Rachid NACIRI
  • Abderrahim MBARKI


b-Menger space, Cauchy sequence, Fixed point


The purpose of this work is to define the generalized b-Menger spaces and prove a fixed point theorem in this new setting. As application, we establish the existence and uniqueness of a solution for Volterra type integral equation.


Bakhtin I. A., The contraction mapping principle in quasi metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26-37.

Czerwik S., Contraction mappings in b-metric space, Acta Math. Inf. Univ. Ostraviensis, 1 (1993), 5-11.

De La Sen M., About some controllability properties of linear discrete-time systems in probabilistic metric spaces. Informatica 27 (2006) 503-526.

Fréchet M., Sur quelques points du calcul fonctionnel. Rendic. Circ. Mat. Palermo 22 1-74 (1906).

Golet I., Carstea H., Negrea R., On approximation of random signals and their usage in electronic packaging, 1st Electrinic System-integration Technology Conference, Dresden, Germany, 2006, pp. 589-593.

Guz W., Stochastic phase spaces, fuzzy sets and statistical metric spaces. Found. Phys. 14 821-848 (1984).

Hadzi´c O., A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) T 20 (1979) 107–112.

Hamed H. Alsulami, Erdal Karapinar, Vladimir Rakoc˜evic´, C´ iric´ type nonunique fixed point theorems on b-metric spaces. Filomat 31:11 (2017), 3147-3156.

Kamran T., Samreen M., Ain ul Q., Ageneralization of b-metric space and some fixed point theorems, Mathematics, 5 (2017), No. 2, Art. No. 19.

Mbarki A. and Naciri R., Probabilistic generalized metric spaces and nonlinear contractions. Demonstr. Math. 49 (4) 437-452 (2016).

Mbarki A. and Oubrahim R., Probabilistic b-metric spaces and nonlinear contractions. Fixed Point Theory and Applications (2017) 2017:29.

Mbarki A. and Oubrahim R., Probabilistic phi-contraction in b-Menger spaces with fully convex structure. International Journal of Applied Mathematics. Volume 33 No. 4, 2020, 621-633.

Mbarki A. and Oubrahim R., Some properties of convexity structure and applications in b-Menger spaces. SEMA SIMAI Springer Series, 2022, 29, pp. 181-189.

Menger K., Statistical metrics. Proc. Nat. Acad. Sci. 28, 535–7 (1942).

Schweizer B. and Sklar A., Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathematics, 5, (1983).

Zoran D. Mitrovic, Fixed point results in b-metric space. Fixed Point Theory, 20 (2019), No. 2, 559-566.




How to Cite

OUBRAHIM, R. ., NACIRI, R., & MBARKI, A. (2023). Fixed point theorems in generalized b-Menger spaces. Results in Nonlinear Analysis, 7(1), 35–43. Retrieved from