On a Generalized Briot-Bouquet type Differential Subordination
Complex Variables
2022-03-14 v2
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 is analytic and 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.
Cite
@article{arxiv.2101.00353,
title = {On a Generalized Briot-Bouquet type Differential Subordination},
author = {S. Sivaprasad Kumar and Priyanka Goel},
journal= {arXiv preprint arXiv:2101.00353},
year = {2022}
}