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arXiv · 2201.01473

Starlikeness of a product of starlike functions with non-vanishing polynomials

Somya Malik·V. Ravichandran
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Abstract

For a function $f$ starlike of order $α$, $0\leqslant α<1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $\mathbb{D}$ and $β>0$, we consider the function $F:\mathbb{D}\to\mathbb{C}$ defined by $F(z)=f(z) (Q(z))^{β/n}$ and find the largest value of $r\in (0,1]$ such that $r^{-1} F(rz)$ lies in various known subclasses of starlike functions such as the class of starlike functions of order $λ$, the classes of starlike functions associated with the exponential function, cardioid, a rational function, nephroid domain and modified sigmoid function. Our radii results are sharp. We also discuss the correlation with known radii results as special cases.

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Somya Malik, V. Ravichandran. 2022-01-05. Starlikeness of a product of starlike functions with non-vanishing polynomials. https://arxiv.org/abs/2201.01473

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