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

نویسندگان

چکیده

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

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ژورنال

عنوان ژورنال: Analysis and Mathematical Physics

سال: 2023

ISSN: ['1664-2368', '1664-235X']

DOI: https://doi.org/10.1007/s13324-023-00794-x