Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2406.13328 |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866910501942853632 |
|---|---|
| author | Dash, Prachi Prajna Prajapat, Jugal Kishore Kumari, Naveen |
| author_facet | Dash, Prachi Prajna Prajapat, Jugal Kishore Kumari, Naveen |
| contents | Let $\mathcal{G}(α)$ denote the family of functions $ f(z)$ in the open unit disk $\mathbb D :=\{z\in\mathbb{C}: |z|<1\}$ that satisfy $ f(0)=0= f'(0)=1$ and \[\Re \left(1+ \dfrac{z f''(z)}{ f'(z)}\right)<1+\dfracα{2} , \quad z\in \mathbb D.\] We determine the disks $|z|<ρ_n$ in which sections $ s_n(z; f)$ of $ f(z)$ are convex, starlike, and close-to-convex of order $β\;(0\le β< 1)$. Further, we obtain certain inequalities of sections in the considered class of functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13328 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radii for sections of functions convex in one direction Dash, Prachi Prajna Prajapat, Jugal Kishore Kumari, Naveen Complex Variables 30C45, 30C20, 30C75, 30C80 Let $\mathcal{G}(α)$ denote the family of functions $ f(z)$ in the open unit disk $\mathbb D :=\{z\in\mathbb{C}: |z|<1\}$ that satisfy $ f(0)=0= f'(0)=1$ and \[\Re \left(1+ \dfrac{z f''(z)}{ f'(z)}\right)<1+\dfracα{2} , \quad z\in \mathbb D.\] We determine the disks $|z|<ρ_n$ in which sections $ s_n(z; f)$ of $ f(z)$ are convex, starlike, and close-to-convex of order $β\;(0\le β< 1)$. Further, we obtain certain inequalities of sections in the considered class of functions. |
| title | Radii for sections of functions convex in one direction |
| topic | Complex Variables 30C45, 30C20, 30C75, 30C80 |
| url | https://arxiv.org/abs/2406.13328 |