109 Navneet Lala Sharma
109 Navneet Lala Sharma
Estimates logarithmic coefficients for certain classes of univalent functions
Abstract
Let $\mathcal{S}$ be the family of analytic and univalent functions $f$ in the unit disk $\mathbb{D}$
with the normalization $f(0)=f'(0)-1=0$.
The logarithmic coefficients $\gamma_n$ of $f\in \mathcal{S}$ are defined by the formula
$$
\log\left(\frac{f(z)}{z}\right)\,=\,2\sum_{n=1}^{\infty}\gamma_n(f)z^n.
$$
In this talk, we will discuss bounds for the logarithmic coefficients for certain geometric subfamilies of univalent functions as starlike, convex, close-to-convex and Janowski starlike functions. Also, we consider the families $\mathcal{F}(c)$ and
$\mathcal{G}(\delta)$ of functions $f\in \mathcal{S}$ defined by
$$ {\rm Re} \left ( 1+\frac{zf''(z)}{f'(z)}\right )>1-\frac{c}{2}\, \mbox{ and } \,
{\rm Re} \left ( 1+\frac{zf''(z)}{f'(z)}\right )<1+\frac{\delta}{2},\quad z\in \mathbb{D} $$
for some $c\in(0,3]$ and $\delta\in (0,1]$, respectively. We obtain the sharp upper bound for $|\gamma_n|$
Rod Halburd | |
35 | |
5/23/2023 | |
00:54:10 | |
CAvid, Complex Analysis |