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arXiv · 1905.05413

Coefficients of the Inverse Functions and Radius Estimates of Certain Starlike Functions

Adiba Naz·Sushil Kumar·V. Ravichandran
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Abstract

Ma-Minda class (of starlike functions) consists of all normalized analytic functions $f$ on the unit disk for which the image of $zf'(z)/f(z)$ is contained in the some starlike region in the right-half plane. We obtain the best possible bounds on the second and third coefficient for the inverse functions of functions in the Ma-Minda class. The bounds on the Fekete-Szeg\"o functional and the second Hankel determinant of the inverse functions of the functions belonging to the Ma-Minda class are also determined. Further, the bounds on the first five coefficients of the inverse functions are investigated for two particular subclasses of the Ma-Minda class. In addition, some radius estimates associated with the two subclasses are also computed.

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Adiba Naz, Sushil Kumar, V. Ravichandran. 2019-05-14. Coefficients of the Inverse Functions and Radius Estimates of Certain Starlike Functions. https://arxiv.org/abs/1905.05413

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