TY - JOUR
T1 - A Note on Successive Coefficients of Convex Functions
AU - Li, Ming
AU - Sugawa, Toshiyuki
N1 - Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - In this note, we investigate the supremum and the infimum of the functional | an + 1| - | an| for functions, convex and analytic on the unit disk, of the form f(z) = z+ a2z2+ a3z3+ ⋯. We also consider the related problem of maximizing the functional | an + 1- an| for convex functions f with f′ ′(0) = p for a prescribed p∈ [0 , 2].
AB - In this note, we investigate the supremum and the infimum of the functional | an + 1| - | an| for functions, convex and analytic on the unit disk, of the form f(z) = z+ a2z2+ a3z3+ ⋯. We also consider the related problem of maximizing the functional | an + 1- an| for convex functions f with f′ ′(0) = p for a prescribed p∈ [0 , 2].
KW - Convex function
KW - Successive coefficients
KW - Toeplitz determinant
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U2 - 10.1007/s40315-016-0177-8
DO - 10.1007/s40315-016-0177-8
M3 - Article
AN - SCOPUS:85019259034
SN - 1617-9447
VL - 17
SP - 179
EP - 193
JO - Computational Methods and Function Theory
JF - Computational Methods and Function Theory
IS - 2
ER -