Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers
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...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/236124 |
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| author | Ahmet Faruk Çakmak Feyzi Başar |
| author_facet | Ahmet Faruk Çakmak Feyzi Başar |
| author_sort | Ahmet Faruk Çakmak |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-9501b6329f764b2ab8569a875f2aa3ab |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-9501b6329f764b2ab8569a875f2aa3ab2025-02-03T01:23:09ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/236124236124Certain Spaces of Functions over the Field of Non-Newtonian Complex NumbersAhmet Faruk Çakmak0Feyzi Başar1Department of Mathematical Engineering, Yıldız Technical University, Davutpaşa Campus, Esenler, 80750 Istanbul, TurkeyDepartment of Mathematics, Faculty of Arts and Sciences, Fatih University, Hadimköy Campus, Büyükçekmece, 34500 Istanbul, TurkeyThis 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.http://dx.doi.org/10.1155/2014/236124 |
| spellingShingle | Ahmet Faruk Çakmak Feyzi Başar Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers Abstract and Applied Analysis |
| title | Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers |
| title_full | Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers |
| title_fullStr | Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers |
| title_full_unstemmed | Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers |
| title_short | Certain Spaces of Functions over the Field of Non-Newtonian Complex Numbers |
| title_sort | certain spaces of functions over the field of non newtonian complex numbers |
| url | http://dx.doi.org/10.1155/2014/236124 |
| work_keys_str_mv | AT ahmetfarukcakmak certainspacesoffunctionsoverthefieldofnonnewtoniancomplexnumbers AT feyzibasar certainspacesoffunctionsoverthefieldofnonnewtoniancomplexnumbers |