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

Ayşe Çobankaya

doi:10.53570/jnt.1845528

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

References

F. Khojasteh, E. Karapınar, S. Radenovic, $\theta$-Metric spaces: A generalization, Mathematical Problems in Engineering 2013 (2013) 504609.
N. Priyobarta, Y. Rohen, S. Radenovic, Fixed point theorems on parametric A-metric space, American Journal of Applied Mathematics and Statistics 6 (1) (2018) 1–5.
N. Taş, N. Y. Özgür, On parametric S-metric spaces and fixed point type theorems for expansive mappings, Journal of Mathematics 2016 (2016) 4746732.
S. Abdullayev, S. Bayramov, C. Gunduz Aras, A study on parametric soft S-metric spaces, Annals of Fuzzy Mathematics and Informatics 28 (1) (2024) 75–83.
L. Pasicki, Cauchy sequences in b-metric spaces, Topology and Its Applications 373 (2025) 109477.
N. Hussain, P. Salimi, V. Parvaneh, Fixed point results for various contractions in parametric and fuzzy b-metric spaces, Journal of Nonlinear Sciences and Applications 8 (5) (2015) 719–739.
A. Moussaoui, S. Radenovic, b-metric like spaces: A survey of concepts and applications, Vojnotehnicki Glasnik 73 (3) (2025) 1068–1097.
A. Moussaoui, S. Radenovic, Fuzzy metric spaces: A survey on fixed point results, contraction principles and simulation functions, Fixed Point Theory and Algorithms for Sciences and Engineering 2025 (2025) 24.

Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Ayşe Çobankaya ^*
0000-0001-9485-9534
Türkiye

Publication Date

March 30, 2026

Submission Date

December 19, 2025

Acceptance Date

March 5, 2026

Published in Issue

Year 2026 Number: 54

DOI

https://doi.org/10.53570/jnt.1845528

IZ

https://izlik.org/JA38JU23BP

Cite

RIS / Bibtex

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