Coefficient estimates for the class of q-starlike functions
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866916889629818880 |
|---|---|
| author | Li, Ming Zhu, Ao-Li |
| author_facet | Li, Ming Zhu, Ao-Li |
| contents | By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations. Inspired by prior research, this paper delves into the class of $q$-starlike functions defined via convolution. First, we provide comprehensive analysis of its Taylor coefficients by using the Carathéodory-Toeplitz Theorem and its corollaries. Precise upper bounds for the initial few coefficients are obtained for real $q\in(0,1)$. Furthermore, we analyze both Hankel and Toeplitz determinants by using the foundational results. Second, we establish the upper bounds of its coefficients with the application of Parseval's theorem for $q$-starlike functions when $q$ is a complex number. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_03223 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Coefficient estimates for the class of q-starlike functions Li, Ming Zhu, Ao-Li Complex Variables 30C45, 30C50 By employing the $q$-difference operator, various classes of $q$-extensions of starlike functions have emerged from many different viewpoints and perspectives. Ruscheweyh's work unified these $q$-extensions with convolution operations. Inspired by prior research, this paper delves into the class of $q$-starlike functions defined via convolution. First, we provide comprehensive analysis of its Taylor coefficients by using the Carathéodory-Toeplitz Theorem and its corollaries. Precise upper bounds for the initial few coefficients are obtained for real $q\in(0,1)$. Furthermore, we analyze both Hankel and Toeplitz determinants by using the foundational results. Second, we establish the upper bounds of its coefficients with the application of Parseval's theorem for $q$-starlike functions when $q$ is a complex number. |
| title | Coefficient estimates for the class of q-starlike functions |
| topic | Complex Variables 30C45, 30C50 |
| url | https://arxiv.org/abs/2508.03223 |