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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/2411.04235 |
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| _version_ | 1866910121363243008 |
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| author | Biswas, Raju Mandal, Rajib |
| author_facet | Biswas, Raju Mandal, Rajib |
| contents | Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradović and Ponnusamy have introduced the class $\mathcal{M}(λ)$ such that the functions in $\mathcal{M}(λ)$ are univalent in $\mathbb{D}$ whenever $0<λ\leq 1$. In this paper, we address a radius property of the class $\mathcal{M}(λ)$ and a number of associated results pertaining to $\mathcal{M}$. The main objective of this paper is to examine the largest disks with sharp radius for which the functions $F$ defined by the relations $g(z)h(z)/z$, $z^2/g(z)$, and $z^2/\int_0^z (t/g(t))dt$ belong to the class $\mathcal{M}$, where $g$ and $h$ belong to some suitable subclasses of $\mathcal{S}$, the class of univalent functions from $\mathcal{A}$. In the final analysis, we obtain the sharp Bohr radius, Bohr-Rogosinski radius and improved Bohr radius for a certain subclass of starlike functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04235 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A geometric investigation of a certain subclass of univalent functions Biswas, Raju Mandal, Rajib Complex Variables 30C45, 30C50, 30C80, 30A10, 30H05 Let $\mathcal{H}$ be the space of all functions that are analytic in $\mathbb{D}$. Let $\mathcal{A}$ denote the family of all functions $f\in\mathcal{H}$ and normalized by the conditions $f(0)=0=f'(0)-1$. Obradović and Ponnusamy have introduced the class $\mathcal{M}(λ)$ such that the functions in $\mathcal{M}(λ)$ are univalent in $\mathbb{D}$ whenever $0<λ\leq 1$. In this paper, we address a radius property of the class $\mathcal{M}(λ)$ and a number of associated results pertaining to $\mathcal{M}$. The main objective of this paper is to examine the largest disks with sharp radius for which the functions $F$ defined by the relations $g(z)h(z)/z$, $z^2/g(z)$, and $z^2/\int_0^z (t/g(t))dt$ belong to the class $\mathcal{M}$, where $g$ and $h$ belong to some suitable subclasses of $\mathcal{S}$, the class of univalent functions from $\mathcal{A}$. In the final analysis, we obtain the sharp Bohr radius, Bohr-Rogosinski radius and improved Bohr radius for a certain subclass of starlike functions. |
| title | A geometric investigation of a certain subclass of univalent functions |
| topic | Complex Variables 30C45, 30C50, 30C80, 30A10, 30H05 |
| url | https://arxiv.org/abs/2411.04235 |