Journals / Avrupa Bilim ve Teknoloji Dergisi / 2026 / Sayı: 28 Özel Sayı

Hyperbolic Valued Dislocated Metric Spaces

Hiperbolik Değerli Dislocated Metrik Uzaylar

Nilay Değirmen(Ondokuz Mayıs University Faculty of Science and Arts)0000-0001-8192-8473
Pages
1152–1158
Publication Date
2021-11-30
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AI Summary & Key Takeaways

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

Furthermore, we discuss an illustrative example to substantiate the applicability and usefulness of our main result.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this work, we introduce the concept of a hyperbolic valued dislocated metric space, and we show that a fixed point of self-mappings in such spaces is exist and unique by using Banach, Kannan and Chatterjea type contractions.
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Key Findings & Data:In this work, we introduce the concept of a hyperbolic valued dislocated metric space, and we show that a fixed point of self-mappings in such spaces is exist and unique by using Banach, Kannan and Chatterjea type contractions.
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Conclusion & Impact:Furthermore, we discuss an illustrative example to substantiate the applicability and usefulness of our main result.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:hiperbolik sayı · dislocated metrik uzay · sabit nokta

Abstract

In this work, we introduce the concept of a hyperbolic valued dislocated metric space, and we show that a fixed point of self-mappings in such spaces is exist and unique by using Banach, Kannan and Chatterjea type contractions. Furthermore, we discuss an illustrative example to substantiate the applicability and usefulness of our main result.

Özet

Bu çalışmada, hiperbolik değerli dislocated metrik uzay kavramını sunduk ve Banach, Kannan ve Chatterjea tip daralmaları kullanarak böyle uzayların kendileri üzerinde tanımlı dönüşümler için bir sabit noktanın var ve tek olduğunu gösterdik. Ayrıca ana sonucumuzun uygulanabilirliğini ve kullanışlılığını ispatlamak için açıklayıcı bir örnek verdik.

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Cite This Article

Değirmen, N. (2021). Hyperbolic Valued Dislocated Metric Spaces. Avrupa Bilim ve Teknoloji Dergisi, Sayı: 28 Özel Sayı, 1152–1158. https://doi.org/10.31590/ejosat.1013323

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References (14)

  1. Banach, S. (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fund. Math., 3(1), 133-181.
  2. Chatterjea, S. K. (1972). Fixed-point theorems. C. R. Acad. Bulgare Sci., 25, 727-730.
  3. Gaba H. & Garg A. K. (2019). Some fixed point results for contraction in dislocated metric space. International Journal on Emerging Technologies, 10(2b), 147-150.
  4. Hitzler, P., & Seda, A. K. (2000). Dislocated topologies. J. Electr. Eng., 51(12), 3-7.
  5. Kannan, R. (1968). Some results on fixed points. Bull. Cal. Math. Soc., 60, 71-76.
  6. Kumar, R., & Saini, H. (2016). Topological bicomplex modules. Advances in Applied Clifford Algebras, 26(4), 1249-1270.
  7. Luna-Elizarrarás, M. E., Shapiro, M., Struppa, D. C., & Vajiac, A. (2015). Bicomplex holomorphic functions: the algebra, geometry and analysis of bicomplex numbers. Birkhäuser.
  8. Pasicki, L. (2015). Dislocated metric and fixed point theorems. Fixed Point Theory and Applications, 2015(1), 1-14.
  9. Price, G. B. (1991). An introduction to multicomplex spaces and functions. M. Dekker.
  10. Rahman, M. U., & Sarwar, M. (2015). Fixed point theorems for expanding mappings in dislocated metric space. Mathematical Sciences Letters, 4(1), 69-73.
  11. Sager, N., & Sağır, B. (2021). Fixed points of hyperbolic contraction mappings on hyperbolic valued metric spaces. Sarajevo Journal of Mathematics, 17(2). (in print)
  12. Sager, N., & Sağır, B. (2021). Common fixed, coupled coincidence and common coupled fixed point results in hyperbolic valued metric spaces. Boletim da Sociedade Paranaense de Matemática. (accepted for publication)
  13. Wadkar, B. R., Bhardwaj, R., & Singh, B. (2017). Some fixed point theorems in dislocated metric space. Global Journal of Pure and Applied Mathematics, 13(6), 2089-2110.
  14. Zeyada, F. M., Hassan, G. H., & Ahmed, M. A. (2006). A generalization of a fixed point theorem due to Hitzler and Seda in dislocated quasi-metric spaces. Arabian Journal for Science and Engineering, 31(1A), 111-114.