Some Results of Common Fixed Point for Compatible Mappings in Ƒ-Metric Spaces

Abstract

Recently, Ƒ-metric space has been started, and a natural topology has been described in these spaces by Jleli and Samet. Furthermore, a new form of the Banach contraction principle has been given in the new spaces. In this work, we present some common fixed-point theorems for two weakly compatible mappings in the Ƒ-metric spaces. We also mention examples that confirm our results.

Keywords

• Common fixed point
• Ƒ-metric space
• weakly compatible

References

1. S. Czerwik, Contraction Mappings in b-Metric Spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1) (1993) 5–11.
2. M. A. Khamsi, N. Hussain, KKM Mapping in Metric Type Spaces, Nonlinear Analysis 7(9) (2010) 3123–3129.
3. R. Fagin, R. Kumar, D. Sivakumar, Comparing Top k Lists, SIAM Journal on Discrete Mathematics 17(1) (2003) 134–160.
4. W. Kirk, N. Shahzad, Fixed Point Theory in Distance Spaces, Springer: Cham, 2014.
5. V. S. Gahler, 2-Metrische Raume und ihre Topologishe Strüktür, Mathematische Nachrichten 26 (1963/1964) 115–118.
6. Z. Mustafa, B. Sims, A New Approach to Generalized Metric Spaces, Journal of Nonlinear and Convex Analysis 7(2) (2006) 289–297.
7. S. G. Matthews, Partial Metric Topology. In: Proceedings of the 8th Summer Conference on General Topology and Applications. Annals of the New York Academy of Sciences 728 (1994) 183–197.
8. M. Jleli, B. Samet, A Generalized Metric Space and Related Fixed-Point Theorems, Fixed Point Theory and Its Applications Article Number 61 (2015) 1–14.

9. M. Jleli, B. Samet, On a New Generalization of Metric Spaces, Journal of Fixed-Point Theory and Applications Article Number 128 20 (2018) 1–20.
10. A. L. Alnaser, D. Lateef, A. H. Fouad, J. Ahmad, Relation Theoretic Contraction Results in Ƒ-Metric Spaces, Journal of Nonlinear Sciences and Applications 12 (2019) 337–344.
11. M. Abbas, G. Jungck, Common Fixed-Point Results for Non-Commuting Mappings without Continuity in Cone Metric Spaces, Journal of Mathematical Analysis and Applications 341 (2008) 416–420.