On the difference of coefficients of univalent functions | Zendy

Milutin Obradović | Zendy; Derek K. Thomas | Zendy; Nikola Tuneski | Zendy

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On the difference of coefficients of univalent functions

Author(s) -

Milutin Obradović,

Derek K. Thomas,

Nikola Tuneski

Publication year - 2021

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil2111653o

Subject(s) - mathematics , unit disk , upper and lower bounds , unit (ring theory) , combinatorics , mathematical analysis , class (philosophy) , analytic function , pure mathematics , mathematics education , artificial intelligence , computer science

For f ? S, the class of normalized functions, analytic and univalent in the unit disk D and given by f(z)=z+?? n=2 an Zn 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.

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