Some inequalities for a certain subclass of starlike functions

R. Kargar; H. Mahzoon; N. Kanzi

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arXiv · 1804.06435

Some inequalities for a certain subclass of starlike functions

R. Kargar·H. Mahzoon·N. Kanzi

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Abstract

In 2011, Sokół (Comput. Math. Appl. 62, 611--619) introduced and studied the class $\mathcal{SK}(α)$ as a certain subclass of starlike functions, consists of all functions $f$ ($f(0)=0=f'(0)-1$) which satisfy in the following subordination relation: \begin{equation*} \frac{zf'(z)}{f(z)}\prec \frac{3}{3+(α-3)z-αz^2} \qquad |z|<1, \end{equation*} where $-3<α\leq1$. Also, he obtained some interesting results for the class $\mathcal{SK}(α)$. In this paper, some another properties of this class, including infimum of $\mathfrak{Re}\frac{f(z)}{z}$, order of strongly starlikeness, the sharp logarithmic coefficients inequality and the sharp Fekete-Szegö inequality are investigated.

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R. Kargar, H. Mahzoon, N. Kanzi. 2018-04-17. Some inequalities for a certain subclass of starlike functions. https://arxiv.org/abs/1804.06435

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