Geometrik kalkülüse göre bikompleks sayılar ve bazı eşitsizlikler

Yıl 2022, Cilt: 38 Sayı: 2, 335 - 348, 23.08.2022

Nilay Değirmen , Birsen Sağır Duyar

Öz

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.

Anahtar Kelimeler

geometrik kalkülüs, non-Newtonian bikompleks sayı, non-Newtonian kompleks sayı, eşitsizlikler

Bicomplex numbers with respect to the geometric calculus and some inequalities

Öz

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.

Anahtar Kelimeler

geometric calculus, non-Newtonian bicomplex number, non-Newtonian complex number, inequalities

Kaynakça

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