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Journals / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 18 Issue: 2

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

Ümran Başar(KIRIKKALE UNIVERSITY)0000-0002-7296-8382
Ahmet Hakan Arslan(KIRIKKALE UNIVERSITY)0000-0003-2632-601X
İshak Altun(KIRIKKALE UNIVERSITY)0000-0002-7967-0554
Pages
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Publication Date
2026-06-30
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

Finally, we briefly discuss how certain metric fixed point theorems from the literature can be derived using the τ-distance framework.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we obtain fixed point results in Hausdorff topological spaces using the notion of τ-distance.
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Key Findings & Data: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.
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Conclusion & Impact:Finally, we briefly discuss how certain metric fixed point theorems from the literature can be derived using the τ-distance framework.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Fixed point · τ-distance · Hausdorff topological space

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.

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Cite This Article

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, Volume: 18 Issue: 2. https://doi.org/10.47000/tjmcs.1850623

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