Majorization problems for certain starlike functions associated with the exponential function

Authors

  • Hesam Mahzoon Department of Mathematics, Islamic Azad University, West Tehran Branch, Tehran, Iran

DOI:

https://doi.org/10.24193/subbmath.2022.4.05

Keywords:

Univalent, Starlike, Exponential function, Majorization, Subordination, Bell numbers.

Abstract

Let $\mathcal{S}^*_e$ and $\mathcal{S}^*_B$ denote the class of analytic functions $f$ in the open unit disc normalized by $f(0)=0=f'(0)-1$ and satisfying, respectively, the following subordination relations:
\begin{equation*}
  \frac{zf'(z)}{f(z)}\prec e^z\quad{\rm and}\quad\frac{zf'(z)}{f(z)}\prec e^{e^z-1}.
\end{equation*}
In this article, we investigate majorization problems for the classes $\mathcal{S}^*_e$ and $\mathcal{S}^*_B$ without acting upon any linear or nonlinear operators.

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Published

2022-12-01

Issue

Section

Articles