English

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 Q(z)Q(z) is analytic and 0β,αC.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.

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}
}
R2 v1 2026-06-23T21:41:47.607Z