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

DOI10.1007/S13324-023-00794-XarXiv2201.01473MaRDI QIDQ6387534

Somya Malik, V. Ravichandran

Publication date: 5 January 2022

Abstract: For a function $f$ starlike of order $alpha$, $0leqslantalpha<1$, a non-constant polynomial $Q$ of degree $n$ which is non-vanishing in the unit disc $mathbbD$ and $$, we consider the function $F:mathbbDomathbbC$ defined by $$ and find the largest value of $rin(0,1]$ such that $r^{-1}F(rz)$ lies in various known subclasses of starlike functions such as the class of starlike functions of order $lambda$, 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.

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Polynomials and rational functions of one complex variable (30C10)

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