On P-Contractions in Hausdorff Spaces with a τ-Distance

Ümran Başar; Ahmet Hakan Arslan; İshak Altun

doi:10.47000/tjmcs.1850623

On P-Contractions in Hausdorff Spaces with a τ-Distance

Abstract

In this paper, we obtain fixed point results in Hausdorff topological spaces using the notion of τ-distance. We introduce a new type of contraction, called a P-contraction, defined on topological spaces equipped with a τ-distance, and establish a fixed point theorem for self-maps satisfying this condition. Assuming that the space is p-bounded and S-complete, and that the mapping is p-τ-continuous, we prove the existence and uniqueness of fixed points for such self-maps. Our results generalize several well-known fixed point theorems in the literature by both weakening the classical assumptions via the topological structure and by extending the contraction condition. In addition to an example that supports this generalization, we present another that highlights the advantages of employing the τ-distance function instead of the standard metric. Finally, we briefly discuss how certain metric fixed point theorems from the literature can be derived using the τ-distance framework.

Keywords

References

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Details

Primary Language

English

Subjects

Topology

Journal Section

Research Article

Authors

Ümran Başar This is me
0000-0002-7296-8382
Türkiye

Ahmet Hakan Arslan This is me
0000-0003-2632-601X
Türkiye

İshak Altun ^*
0000-0002-7967-0554
Türkiye

Publication Date

June 30, 2026

Submission Date

December 28, 2025

Acceptance Date

February 2, 2026

Published in Issue

Year 2026 Volume: 18 Number: 2

DOI

https://doi.org/10.47000/tjmcs.1850623

IZ

https://izlik.org/JA57ZX89ZS

Cite

RIS / Bibtex

APA

Başar, Ü., Arslan, A. H., & Altun, İ. (2026). On P-Contractions in Hausdorff Spaces with a τ-Distance. Turkish Journal of Mathematics and Computer Science, 18(2), 440-449. https://doi.org/10.47000/tjmcs.1850623

AMA

1.Başar Ü, Arslan AH, Altun İ. On P-Contractions in Hausdorff Spaces with a τ-Distance. TJMCS. 2026;18(2):440-449. doi:10.47000/tjmcs.1850623

Chicago

Başar, Ümran, Ahmet Hakan Arslan, and İshak Altun. 2026. “On P-Contractions in Hausdorff Spaces With a τ-Distance”. Turkish Journal of Mathematics and Computer Science 18 (2): 440-49. https://doi.org/10.47000/tjmcs.1850623.

EndNote

Başar Ü, Arslan AH, Altun İ (June 1, 2026) On P-Contractions in Hausdorff Spaces with a τ-Distance. Turkish Journal of Mathematics and Computer Science 18 2 440–449.

IEEE

[1]Ü. Başar, A. H. Arslan, and İ. Altun, “On P-Contractions in Hausdorff Spaces with a τ-Distance”, TJMCS, vol. 18, no. 2, pp. 440–449, June 2026, doi: 10.47000/tjmcs.1850623.

ISNAD

Başar, Ümran - Arslan, Ahmet Hakan - Altun, İshak. “On P-Contractions in Hausdorff Spaces With a τ-Distance”. Turkish Journal of Mathematics and Computer Science 18/2 (June 1, 2026): 440-449. https://doi.org/10.47000/tjmcs.1850623.

JAMA

1.Başar Ü, Arslan AH, Altun İ. On P-Contractions in Hausdorff Spaces with a τ-Distance. TJMCS. 2026;18:440–449.

MLA

Başar, Ümran, et al. “On P-Contractions in Hausdorff Spaces With a τ-Distance”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 2, June 2026, pp. 440-9, doi:10.47000/tjmcs.1850623.

Vancouver

1.Ümran Başar, Ahmet Hakan Arslan, İshak Altun. On P-Contractions in Hausdorff Spaces with a τ-Distance. TJMCS. 2026 Jun. 1;18(2):440-9. doi:10.47000/tjmcs.1850623