Dual-Variable Functions on Time Scale

Year 2018, , 265 - 278, 30.09.2018

Hatice Kuşak Samancı

https://doi.org/10.21597/jist.458652

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

References

• Aktan N, Sarikaya M, Ilarslan K, Yildirim H, 2009. Directional Nabla-derivative and Curves on n-dimensional Time Scales, Acta Appl. Math, (105), 45-63.
• Aulbach B, Hilger S, 1990. Linear Dynamic Processes with in Homogeneous Time Scale, Nonlinear Dynamics and Quantum Dynamical System, Berlin Academia Verlag, 9-20.
• Bohner M, Peterson A, 2001. Dynamic Equations on timescales, An Introduction with Applications, Birkhӓuser.
• Bohner M, Guseinov G, 2006. An introduction to complex functions on products of two time scales, Journal of Difference Equations and Applications, (12), 369-384.
• Ercan Z, Yuce S, 2011. On properties of dual quaternions, Eur. J. Pure Appl. Math., (4) No.2, 142-146.
• Hilger S, 1990. Analysis on Measure Chains-a Unified Approach to Continuous and Discrete Calculus, Results math., (18), 18-56.
• Kramer EE, 1930. Polygenic functions of the dual variable, Amer. J. Math., (52), No.2, 370-376.
• Messelmi F, 2013. Analysis of Dual Functions, Annual Review of Chaos Theory, Bifurcations and Dynamical Systems, Mechanisms and Machine Theory, (4), 37-54.
• Onder M, Ugurlu HH, 2013. Normal and Spherical Curves in Dual space Mediterr. J.Math (10), 1527-1537.
• Study E, 1901. Geometrie der dynamen, Teubner, Leipzig.
• Veldkamp GR, 1976. On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and Machine Theory, (11), 141-156.
• Yaglom IM, 1969. A Simple Non- Euclidean Geometry and Its Physical Basis.