Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator
In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/17/3064 |
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| author | Ekram Elsayed Ali Mohamed Kamal Aouf Rabha Mohamed El-Ashwah Teodor Bulboacă |
| author_facet | Ekram Elsayed Ali Mohamed Kamal Aouf Rabha Mohamed El-Ashwah Teodor Bulboacă |
| author_sort | Ekram Elsayed Ali |
| collection | DOAJ |
| description | In this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions. |
| first_indexed | 2024-03-10T01:33:30Z |
| format | Article |
| id | doaj.art-52bedd20db8747a5a328bc4934c381f1 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T01:33:30Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-52bedd20db8747a5a328bc4934c381f12023-11-23T13:37:43ZengMDPI AGMathematics2227-73902022-08-011017306410.3390/math10173064Some Subclasses of Spirallike Multivalent Functions Associated with a Differential OperatorEkram Elsayed Ali0Mohamed Kamal Aouf1Rabha Mohamed El-Ashwah2Teodor Bulboacă3Department of Mathematics, Faculty of Science, University of Hail, Hail 81451, Saudi ArabiaDepartment of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Damietta University, New Damietta 34517, EgyptFaculty of Mathematics and Computer Science, Babeş-Bolyai University, 400084 Cluj-Napoca, RomaniaIn this paper we study convolution properties of spirallike multivalent functions defined by using a differential operator and higher order derivatives. Using convolution product relations we determine necessary and sufficient conditions for multivalent functions to belong to these classes, and our results generalized many previous results obtained by different authors. We obtain convolution and inclusion properties for new subclasses of multivalent functions defined by using the Dziok-Srivatava operator. Moreover, using a result connected with the Briot-Bouquet differential subordination, we obtain an inclusion relation between some of these classes of functions.https://www.mdpi.com/2227-7390/10/17/3064analytic functionconvolution productgeneralized hypergeometric functionDziok-Srivastava linear operatorspirallike functiondifferential subordination |
| spellingShingle | Ekram Elsayed Ali Mohamed Kamal Aouf Rabha Mohamed El-Ashwah Teodor Bulboacă Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator Mathematics analytic function convolution product generalized hypergeometric function Dziok-Srivastava linear operator spirallike function differential subordination |
| title | Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator |
| title_full | Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator |
| title_fullStr | Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator |
| title_full_unstemmed | Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator |
| title_short | Some Subclasses of Spirallike Multivalent Functions Associated with a Differential Operator |
| title_sort | some subclasses of spirallike multivalent functions associated with a differential operator |
| topic | analytic function convolution product generalized hypergeometric function Dziok-Srivastava linear operator spirallike function differential subordination |
| url | https://www.mdpi.com/2227-7390/10/17/3064 |
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