Research Article

Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces

Number: 54 March 30, 2026

Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces

Abstract

This paper proposes quasi-Cauchy sequences in $\theta$-parametric metric spaces, a generalized metric framework introduced by Moussaoui et al. in 2024. It establishes fundamental relationships among convergent, Cauchy, and quasi-Cauchy sequences, and puts forward concepts of ward compactness and ward continuity in $\theta$-parametric metric spaces. Moreover, the present paper demonstrates that ward continuity on a ward-compact subset in which every quasi-Cauchy sequence admits a convergent subsequence implies ordinary continuity, that uniformly continuous functions are necessarily ward continuous, and that uniform limits of ward-continuous functions preserve ward continuity. Consequently, all ward-continuous functions on $E$ form a closed set of continuous functions on $E$.

Keywords

Quasi-Cauchy sequences, parametric metric spaces, compactness

References

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APA
Çobankaya, A. (2026). Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces. Journal of New Theory, 54, 49-55. https://doi.org/10.53570/jnt.1845528
AMA
1.Çobankaya A. Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces. JNT. 2026;(54):49-55. doi:10.53570/jnt.1845528
Chicago
Çobankaya, Ayşe. 2026. “Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces”. Journal of New Theory, nos. 54: 49-55. https://doi.org/10.53570/jnt.1845528.
EndNote
Çobankaya A (March 1, 2026) Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces. Journal of New Theory 54 49–55.
IEEE
[1]A. Çobankaya, “Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces”, JNT, no. 54, pp. 49–55, Mar. 2026, doi: 10.53570/jnt.1845528.
ISNAD
Çobankaya, Ayşe. “Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces”. Journal of New Theory. 54 (March 1, 2026): 49-55. https://doi.org/10.53570/jnt.1845528.
JAMA
1.Çobankaya A. Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces. JNT. 2026;:49–55.
MLA
Çobankaya, Ayşe. “Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces”. Journal of New Theory, no. 54, Mar. 2026, pp. 49-55, doi:10.53570/jnt.1845528.
Vancouver
1.Ayşe Çobankaya. Quasi-Cauchy Sequences on $\theta$-Parametric Metric Spaces. JNT. 2026 Mar. 1;(54):49-55. doi:10.53570/jnt.1845528