COMMON FIXED POINT THEOREMS IN b-MENGER SPACES

Abstract

In this work, we prove a common xed point theorem in b-Menger spaces for nonlinear contractions. An example is provided to illustrate this result.

Keywords

• b-Menger space,Common xed point,Nonlinear contraction

References

1. Bakhtin I.A., Contracting mapping principle in an almost metric space. (Russian) Funkts. Anal. 30, 26-37 (1989).
2. Banach S., Sur les operations dans les ensembles abstraits et leur applications aux equations integrales. Fundam. Maths. 3, 133-181 (1922).
3. Czerwik S., Nonlinear set-valued contraction mappings in b-metric spaces, Att Sem Math Univ. Modena 46(2), 263-276, (1998).
4. Elamrani M., Mbarki A. and Mehdaoui B., Nonlinear contarctions and semigroups in general complete probabilistic metric spaces, Panam. Math. J. 11, 4, pp. 79-87, (2001).
5. Hadzic O., A fixed point theorem in Menger spaces, Publ. Inst. Math. (Beograd) T 20, 107-112, (1979).
6. Mbarki A. and Oubrahim R., Probabilistic b-metric spaces and nonlinear contractions. Fixed Point Theory and Applications (2017) 2017: 29.
7. Menger K., Statistical metrics, Proc. Natl. Acad. Sci. 28, 535-537, (1942).
8. Schweizer B. and Sklar A., Probabilistic Metric Spaces, North-Holland Series in Probability and Applied Mathimatics, 5, (1983).

9. Sehgal V. M. and Bharucha-Reid A. T., Fixed point theorems of contractions mappings in probabilistic metric spaces , Math. Systemes Theory, 6, 97-102, (1972).