Geodesic
On the difference of coefficients of univalent functions
Filomat, Tome 35 (2021) no. 11, p. 3653

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DOI

For f ∈ S, the class of normalized functions, analytic and univalent in the unit diskD and given by f (z) = z + ∑∞ n=2 anzn for z ∈ D, we give an upper bound for the coefficient difference |a4| − |a3|when f ∈ S. This provides an improved bound in the case n = 3 of Grinspan’s 1976 general bound ||an+1| − |an|| ≤ 3.61 . . . . Other coefficients bounds, and bounds for the second and third Hankel determinants when f ∈ S are found when either a2 = 0, or a3 = 0
DOI : 10.2298/FIL2111653O
Classification : 30C45, 30C50, 30C55
Keywords: Univalent Functions, Grunsky Coefficients, Coefficient Differences 
Milutin Obradović; Derek K Thomas; Nikola Tuneski. On the difference of coefficients of univalent functions. Filomat, Tome 35 (2021) no. 11, p. 3653 . doi: 10.2298/FIL2111653O
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     title = {On the difference of coefficients of univalent functions},
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     year = {2021},
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     doi = {10.2298/FIL2111653O},
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     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2111653O/}
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