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2014 Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers
Ahmet Faruk Çakmak, Feyzi Başar
Abstr. Appl. Anal. 2014(SI26): 1-12 (2014). DOI: 10.1155/2014/236124


This paper is devoted to investigate some characteristic features of complex numbers and functions in terms of non-Newtonian calculus. Following Grossman and Katz, (Non-Newtonian Calculus, Lee Press, Piegon Cove, Massachusetts, 1972), we construct the field * of * -complex numbers and the concept of * -metric. Also, we give the definitions and the basic important properties of * -boundedness and * -continuity. Later, we define the space C * ( Ω ) of * -continuous functions and state that it forms a vector space with respect to the non-Newtonian addition and scalar multiplication and we prove that C * ( Ω ) is a Banach space. Finally, Multiplicative calculus (MC), which is one of the most popular non-Newtonian calculus and created by the famous exp function, is applied to complex numbers and functions to investigate some advance inner product properties and give inclusion relationship between C * ( Ω ) and the set of C * ( Ω ) * -differentiable functions.


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Ahmet Faruk Çakmak. Feyzi Başar. "Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers." Abstr. Appl. Anal. 2014 (SI26) 1 - 12, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07021969
MathSciNet: MR3198166
Digital Object Identifier: 10.1155/2014/236124

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI26 • 2014
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