Radius of concavity for certain class of functions

Molla Basir Ahamed; Rajesh Hossain

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arXiv · 2407.00457

Radius of concavity for certain class of functions

Molla Basir Ahamed·Rajesh Hossain

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Abstract

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):=\lambda_1f_1(z)+\cdots+\lambda_{2n} f_{2n}(z),\; \lambda_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.

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Molla Basir Ahamed, Rajesh Hossain. 2024-06-29. Radius of concavity for certain class of functions. https://arxiv.org/abs/2407.00457

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