Open AccessOn the difference of coefficients of univalent functions
Author(s) -
Milutin Obradović,
D. 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.