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Journals / Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi / 2026 / Cilt: 38 Sayı: 2

Bicomplex numbers with respect to the geometric calculus and some inequalities

Geometrik kalkülüse göre bikompleks sayılar ve bazı eşitsizlikler

Nilay Değirmen(ONDOKUZ MAYIS UNIVERSITY)0000-0001-8192-8473
Birsen Sağır Duyar(ONDOKUZ MAYIS UNIVERSITY)
Pages
335–348
Publication Date
2022-08-23
DOI
—
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AI Summary & Key Takeaways

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

This paper is a new and important addition to the current literature thanks to its applications in different areas and the obtained results unify, private and complement the corresponding results.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we deal with complex and bicomplex numbers with respect to the geometric calculus, and we obtain the set of complex numbers with respect to the geometric calculus C(GC) is a field and the set of bicomplex numbers with respect to the geometric calculus BC(GC) is a vector space on the field C(GC) by defining addition and multiplication operations on the sets of such numbers.
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Key Findings & Data:Also, we give the concepts of norm, metric, sequence, convergence of a sequence, Cauchy sequence and completeness in the settings C(GC) and BC(GC) .
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Conclusion & Impact:This paper is a new and important addition to the current literature thanks to its applications in different areas and the obtained results unify, private and complement the corresponding results.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:geometrik kalkülüs · non-Newtonian bikompleks sayı · non-Newtonian kompleks sayı

Abstract

In this paper, we deal with complex and bicomplex numbers with respect to the geometric calculus, and we obtain the set of complex numbers with respect to the geometric calculus C(GC) is a field and the set of bicomplex numbers with respect to the geometric calculus BC(GC) is a vector space on the field C(GC) by defining addition and multiplication operations on the sets of such numbers. Also, we give the concepts of norm, metric, sequence, convergence of a sequence, Cauchy sequence and completeness in the settings C(GC) and BC(GC) . Moreover, we discuss bicomplex versions with respect to geometric calculus of some well-known inequalities. This paper is a new and important addition to the current literature thanks to its applications in different areas and the obtained results unify, private and complement the corresponding results.

Özet

Bu makalede, geometrik kalkülüse göre kompleks sayıları ve bikompleks sayıları ele aldık ve böyle sayılardan oluşan kümeler üzerinde toplama ve çarpma işlemlerini tanımlayarak geometrik kalkülüse göre C(GC) kompleks sayılar kümesinin bir cisim olduğunu ve geometrik kalkülüse göre BC(GC) bikompleks sayılar kümesinin C(GC) cismi üzerinde bir vektör uzayı olduğunu elde ettik. Ayrıca C(GC) ve BC(GC) kurulumlarında norm, metrik, dizi, dizinin yakınsaklığı, Cauchy dizisi ve tamlık kavramlarını verdik. Diğer yandan, bazı iyi bilinen eşitsizliklerin geometrik kalkülüse göre bikompleks versiyonlarını tartıştık. Bu makale, farklı alanlardaki uygulamaları ve elde edilen sonuçların birleştirilmesi, özelleştirilmesi ve ilgili sonuçları tamamlaması sayesinde mevcut literatüre yeni ve önemli bir katkıdır.

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Cite This Article

Değirmen, N., Duyar, B. S. (2022). Bicomplex numbers with respect to the geometric calculus and some inequalities. Erciyes Üniversitesi Fen Bilimleri Enstitüsü Fen Bilimleri Dergisi, Cilt: 38 Sayı: 2, 335–348. https://ajindex.com/articles/1266804

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