Some application of Grunsky coefficients in the theory of univalent functions
Keywords:
Sunivalent functions, Grunsky coefficients, third logarithmic coefficient, coefficient difference, generalised Zalcman conjecture, second Hankel determinant, third Hankel determinantAbstract
Let function f be normalized, analytic and univalent in the unit disk D={z: |z|<1} and f(z)=z+∑∞n=2 an zn. Using a method based on Grusky coefficients we study several problems over that class of univalent functions: upper bounds of the special case of the generalized Zalcman conjecture |a2a3-a4|, of the third logarithmic coefficient, and of the second Hankel determinant for the logarithmic coefficients.
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