Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution
UDC 517.53 By using beta-negative binomial distribution, we introduce two novel subclasses of spiral-like functions; namely, spiral-starlike functions and spiral-convex functions denoted by $S^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta)$ and $E^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta),$ respec...
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| Datum: | 2026 |
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| Hauptverfasser: | , , |
| Format: | Artikel |
| Sprache: | Englisch |
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Institute of Mathematics, NAS of Ukraine
2026
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9343 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1862133844586528768 |
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| author | Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. |
| author_facet | Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. |
| author_sort | Pattnayak, Eureka |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-04-10T11:58:56Z |
| description | UDC 517.53
By using beta-negative binomial distribution, we introduce two novel subclasses of spiral-like functions; namely, spiral-starlike functions and spiral-convex functions denoted by $S^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta)$ and $E^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta),$ respectively, and defined in the domain of open unit disk $\mathbb{D}=\{z \in \mathbb{C}\colon |z|<1\}.$ We establish sufficient conditions for functions to be members of families mentioned above. Further, the bounds of some initial coefficients and Fekete–Szegö functionals for the classes described above are obtained. |
| doi_str_mv | 10.3842/umzh.v78i3-4.9343 |
| first_indexed | 2026-03-29T01:00:26Z |
| format | Article |
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| id | umjimathkievua-article-9343 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-04-11T01:00:21Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-93432026-04-10T11:58:56Z Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Analytic function Subordination Fekete-Szego functional Spiral-like function UDC 517.53 By using beta-negative binomial distribution, we introduce two novel subclasses of spiral-like functions; namely, spiral-starlike functions and spiral-convex functions denoted by $S^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta)$ and $E^{\eta}_{\lambda, \gamma, \mu}(\alpha, \beta),$ respectively, and defined in the domain of open unit disk $\mathbb{D}=\{z \in \mathbb{C}\colon |z|<1\}.$ We establish sufficient conditions for functions to be members of families mentioned above. Further, the bounds of some initial coefficients and Fekete–Szegö functionals for the classes described above are obtained. УДК 517.53 Властивості підкласів спіральних функцій з використанням бета-негативного біноміального розподілу З використанням бета-від'ємного біноміального розподілу ввведено два нові підкласи спіральних функцій, а саме: спірале-зіркоподібні функції та спірале-опуклі функції, позначені відповідно $S^{\eta}{\lambda, \gamma, \mu}(\alpha, \beta)$ і $E^{\eta}{\lambda, \gamma, \mu}(\alpha, \beta)$, що визначені в області одиничного круга $\mathbb{D}={z \in \mathbb{C}\colon |z|<1}.$ Встановлено достатні умови для того, щоб функція належала до цих сімей. Крім того, знайдено оцінки для деяких початкових коефіцієнтів і функціоналів Фекете–Сегьо для зазначених класів. Institute of Mathematics, NAS of Ukraine 2026-04-03 Article Article https://umj.imath.kiev.ua/index.php/umj/article/view/9343 10.3842/umzh.v78i3-4.9343 Ukrains’kyi Matematychnyi Zhurnal; Vol. 78 No. 3-4 (2026); 211 Український математичний журнал; Том 78 № 3-4 (2026); 211 1027-3190 en https://umj.imath.kiev.ua/index.php/umj/article/view/9343/10636 Copyright (c) 2026 Eureka Pattnayak, Trailokya Panigrahi, Rabha M. El-Ashwah |
| spellingShingle | Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Pattnayak, Eureka Panigrahi, Trailokya El-Ashwah, Rabha M. Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_alt | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_full | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_fullStr | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_full_unstemmed | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_short | Some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| title_sort | some properties of subclasses of spiral-like functions involving beta-negative binomial distribution |
| topic_facet | Analytic function Subordination Fekete-Szego functional Spiral-like function |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9343 |
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