Dual-Variable Functions on Time Scale

Abstract

In this paper, we study the concept of dual-variable functions parameterized by the product of

two arbitrary time scales. Firstly, we give some preliminaries of the dual numbers and dual-variable functions.

Secondly, we introduce some properties of the time scales. In the main result, we investigate the limit, derivative,

partial differentiation and Cauchy-Riemann equation of the dual-variable functions on time scales.

Keywords

• Cauchy-Riemann equation,dual space,dual-variable functions,time scales

Zaman Skalasında Dual Değişkenli Fonksiyonlar

Abstract

Bu çalışmada, iki keyfi zaman skalasının çarpımı ile parametrelendirilmiş dual değişkenli fonksiyonlar

konusunu inceledik. İlk olarak dual sayıları ve dual değişkenli fonksiyonların bazı özelliklerini verdik. İkinci

olarak zaman skalasının bazı özelliklerini tanıttık. Ana sonuçlar kısmında dual değişkenli fonksiyonların limit,

türev, kısmi diferensiyel ve Cauchy-Riemann denklemini araştırdık.

Keywords

• Cauchy-Riemann denklemi,dual değişkenli fonksiyonlar,dual uzay,zaman skalası

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