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Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers

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  • Ahmet Faruk Çakmak
  • Feyzi Başar

Abstract

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 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 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 and the set of -differentiable functions.

Suggested Citation

  • Ahmet Faruk Çakmak & Feyzi Başar, 2014. "Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, April.
    • Handle: RePEc:hin:jnlaaa:236124
    DOI: 10.1155/2014/236124
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    Cited by:

    1. Cenap Duyar & Birsen Sağır, 2017. "Non-Newtonian Comment of Lebesgue Measure in Real Numbers," Journal of Mathematics, Hindawi, vol. 2017, pages 1-4, February.
    2. Uğur Kadak & Yusuf Gürefe, 2016. "A Generalization on Weighted Means and Convex Functions with respect to the Non-Newtonian Calculus," International Journal of Analysis, Hindawi, vol. 2016, pages 1-9, November.

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