Properties of a Linear Operator Involving Lambert Series and Rabotnov Function
This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient...
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2024/3657721 |
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| author | Jamal Salah |
| author_facet | Jamal Salah |
| author_sort | Jamal Salah |
| collection | DOAJ |
| description | This work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis. |
| format | Article |
| id | doaj-art-c77f82938bbd4aa7ae6a0165c2ea5f1a |
| institution | DOAJ |
| issn | 1687-0425 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-c77f82938bbd4aa7ae6a0165c2ea5f1a2025-08-20T03:05:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences1687-04252024-01-01202410.1155/2024/3657721Properties of a Linear Operator Involving Lambert Series and Rabotnov FunctionJamal Salah0College of Applied and Health SciencesThis work is an attempt to apply Lambert series in the theory of univalent functions. We first consider the Hadamard product of Rabotnov function and Lambert series with coefficients derived from the arithmetic function σn to introduce a normalized linear operator JRα,βz. We then acquire sufficient conditions for JRα,βz to be univalent, starlike and convex, respectively. Furthermore, we discuss the inclusion results in some special classes, namely, spiral-like and convex spiral-like subclasses. In addition, we extend the findings by incorporating two Robin’s inequalities, one of which is analogous to the Riemann hypothesis.http://dx.doi.org/10.1155/2024/3657721 |
| spellingShingle | Jamal Salah Properties of a Linear Operator Involving Lambert Series and Rabotnov Function International Journal of Mathematics and Mathematical Sciences |
| title | Properties of a Linear Operator Involving Lambert Series and Rabotnov Function |
| title_full | Properties of a Linear Operator Involving Lambert Series and Rabotnov Function |
| title_fullStr | Properties of a Linear Operator Involving Lambert Series and Rabotnov Function |
| title_full_unstemmed | Properties of a Linear Operator Involving Lambert Series and Rabotnov Function |
| title_short | Properties of a Linear Operator Involving Lambert Series and Rabotnov Function |
| title_sort | properties of a linear operator involving lambert series and rabotnov function |
| url | http://dx.doi.org/10.1155/2024/3657721 |
| work_keys_str_mv | AT jamalsalah propertiesofalinearoperatorinvolvinglambertseriesandrabotnovfunction |