Using Grunsky coefficients, the authors prove new upper bounds |H2(2)| <= 1.3614... and |H3(1)| <= 1.6787... for the class S of univalent functions.
New upper bounds of the third Hankel determinant for some classes of univalent functions
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abstract
In this paper we give improved, probably not sharp, upper bounds of the Hankel determinant of third order for various classes of univalent functions and conjecture the sharp one.
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An improvement of the estimates of the modulus of the Hankel determinants of second and third order for the class $\mathcal{S}$ of univalent functions
Using Grunsky coefficients, the authors prove new upper bounds |H2(2)| <= 1.3614... and |H3(1)| <= 1.6787... for the class S of univalent functions.