Abstract
In this paper, we establish the coefficient bodies for a wide class of families of inverse functions. We also completely describe functions that are boundary points of these bodies in small dimensions. We use this to obtain sharp bounds for the Fekete–Szegö functionals over some classes of functions defined by quasi-subordination as well as over classes of their inverses. As a biproduct, we derive a formula for ordinary Bell polynomials that seems to be new.
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Elin, M., Jacobzon, F. Families of Inverse Functions: Coefficient Bodies and the Fekete–Szegö Problem. Mediterr. J. Math. 19, 93 (2022). https://doi.org/10.1007/s00009-022-02017-2
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DOI: https://doi.org/10.1007/s00009-022-02017-2