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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2406.13298 |
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| _version_ | 1866911926272917504 |
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| author | Dash, Prachi Prajna Prajapat, Jugal Kishore |
| author_facet | Dash, Prachi Prajna Prajapat, Jugal Kishore |
| contents | For the family of analytic functions $f(z)$ in the open unit disk $\mathbb{D}$ with $f(0)=f'(0)-1=0$, satisfying the differential equation \begin{equation*} zf'(z) - f(z) = \dfrac{1}{2} z^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} we obtain radii of convexity, starlikeness, and close-to-convexity of partial sums of $f(z)$. We also study the generalization of this family having the form \begin{equation*} zf'(z)-f(z) = λz^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} where $λ> 0,$ and obtain some useful properties of these functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_13298 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On certain analytic functions defined by differential inequality Dash, Prachi Prajna Prajapat, Jugal Kishore Complex Variables 30C45 For the family of analytic functions $f(z)$ in the open unit disk $\mathbb{D}$ with $f(0)=f'(0)-1=0$, satisfying the differential equation \begin{equation*} zf'(z) - f(z) = \dfrac{1}{2} z^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} we obtain radii of convexity, starlikeness, and close-to-convexity of partial sums of $f(z)$. We also study the generalization of this family having the form \begin{equation*} zf'(z)-f(z) = λz^2 ϕ(z), \quad |ϕ(z)| \leq 1, \end{equation*} where $λ> 0,$ and obtain some useful properties of these functions. |
| title | On certain analytic functions defined by differential inequality |
| topic | Complex Variables 30C45 |
| url | https://arxiv.org/abs/2406.13298 |