For a function *f* starlike of order *\alpha*, *0\leqslant \alpha <1*, a non-constant polynomial *Q* of degree *n* which is non-vanishing in the unit disc *\mathbb{D}* and *\beta>0*, we consider the function *F:\mathbb{D}\to\mathbb{C}* defined by *F(z)=f(z) (Q(z))^{\beta /n}* and find the largest value of *r\in (0,1]* such that *r^{-1} F(rz)*... Show more

January 5, 2022

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

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