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arXiv · 2101.00353

On a Generalized Briot-Bouquet type Differential Subordination

S. Sivaprasad Kumar·Priyanka Goel
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Abstract

We introduce and study the following special type of differential subordination implication: \begin{equation}\label{abs} p(z)Q(z)+\frac{zp'(z)}{\beta p(z)+\alpha}\prec h(z)\quad\Rightarrow p(z)\prec h(z), \end{equation} which generalizes the Briot-Bouquet differential subordination, where $Q(z)$ is analytic and $0\neq\beta,\alpha\in\mathbb{C}.$ Further, some special cases of our result are also discussed. Finally, analogues of open door lemma and integral existence theorem with applications to univalent functions are obtained.

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S. Sivaprasad Kumar, Priyanka Goel. 2021-01-02. On a Generalized Briot-Bouquet type Differential Subordination. https://arxiv.org/abs/2101.00353

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