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Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers
Joint Authors
Çakmak, Ahmet Faruk
Başar, Feyzi
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-12, 12 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-04-15
Country of Publication
Egypt
No. of Pages
12
Main Subjects
Abstract EN
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 ℂ* 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.
American Psychological Association (APA)
Çakmak, Ahmet Faruk& Başar, Feyzi. 2014. Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers. Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1013516
Modern Language Association (MLA)
Çakmak, Ahmet Faruk& Başar, Feyzi. Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers. Abstract and Applied Analysis No. 2014 (2014), pp.1-12.
https://search.emarefa.net/detail/BIM-1013516
American Medical Association (AMA)
Çakmak, Ahmet Faruk& Başar, Feyzi. Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers. Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-12.
https://search.emarefa.net/detail/BIM-1013516
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1013516