Convergence theorems in new generalized type of metric spaces and their applications ∗

M A  Ahmed; A Kamal; Asmaa M  Abd-Ela

doi:10.48165/bpas.2023.42E.2.6

Authors

M A Ahmed Department of Mathematics, Faculty of Science, Majmaah University, Al-Zulfi, Saudi Arabia.
A Kamal Department of Mathematics, College of Sciences and Arts at Muthnib, Qassim University, Saudi Arabia.
Asmaa M Abd-Ela Department of Mathematics, Faculty of Science, Port Said University, Port Said 42521, Egypt.

DOI:

https://doi.org/10.48165/bpas.2023.42E.2.6

Keywords:

Convergence theorems, q-metric space, rq-metric space

Abstract

In the present paper we introduce a new generalized type of metric spaces called the right quasi-metric spaces. We state and prove convergence theorems to a fixed point for any map in these spaces. Finally, we give applications of our results. These results generalize the corresponding results in M. A. Ahmed and F. M. Zeyada (On con vergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 274(1), 458–465, 2002).

References

Ahmed, M. A. and Zeyada, F. M. (2002). On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. Math. Anal. Appl., 274(1), 458–465.

Ahmed, M. A. and Zeyada, F. M. (2012). Generalization of some results to quasi-metric spaces and its applications, Bulletin of International Mathematical Virtual Institute, 2, 101–107. [3] Aubin, J.-P. (1977). Applied Abstract Analysis, Wiley, New York.

Waszkiewicz, P. (2003). The local triangle axioms in topology and domain theory, Applied General Topology, 4(1), 47–70.