Radius of concavity for certain class of functions
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909234690523136 |
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| author | Ahamed, Molla Basir Hossain, Rajesh |
| author_facet | Ahamed, Molla Basir Hossain, Rajesh |
| contents | Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In this paper, we find radius of concavity and compute the same for functions in $ \mathcal{S}(p) $ and for some other well-known classes of functions on unit disk. We explore general linear combinations $F(z):=λ_1f_1(z)+\cdots+λ_{2n} f_{2n}(z),\; λ_j\in\mathbb{C} $, $ n\in\mathbb{N} $, of functions belonging to the class $\mathcal{S}(p)$ and some other classes of functions of analytic univalent functions and investigate their radii of univalence, convexity and concavity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_00457 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Radius of concavity for certain class of functions Ahamed, Molla Basir Hossain, Rajesh Complex Variables 30C45, 30C55 Let $ \mathcal{S}(p) $ be the class of all meromorphic univalent functions defined in the unit disc $ \mathbb{D} $ of the complex plane with a simple pole at $ z=p $ and normalized by the conditions $ f(0)=0 $ and $ f^{\prime}(0)=1 $. In this paper, we find radius of concavity and compute the same for functions in $ \mathcal{S}(p) $ and for some other well-known classes of functions on unit disk. We explore general linear combinations $F(z):=λ_1f_1(z)+\cdots+λ_{2n} f_{2n}(z),\; λ_j\in\mathbb{C} $, $ n\in\mathbb{N} $, of functions belonging to the class $\mathcal{S}(p)$ and some other classes of functions of analytic univalent functions and investigate their radii of univalence, convexity and concavity. |
| title | Radius of concavity for certain class of functions |
| topic | Complex Variables 30C45, 30C55 |
| url | https://arxiv.org/abs/2407.00457 |