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