Abstract
AbstractIn the paper we consider a general inequality $$|p_{n-1}p_{n+1}-p_n{}^2|\le 4-|p_1|^2$$
|
p
n
-
1
p
n
+
1
-
p
n
2
|
≤
4
-
|
p
1
|
2
involving coefficients of functions with a positive real part. We prove this inequality for $$n=2$$
n
=
2
and $$n=3$$
n
=
3
. Consequently, the relative inequalities involving coefficients of Schwarz functions are obtained. As an application, the two sharp estimates of the Hankel determinants $$H_{3,1}$$
H
3
,
1
and $$H_{2,3}$$
H
2
,
3
are proved for functions in $${\mathcal S}^*(1/2)$$
S
∗
(
1
/
2
)
and $${\mathcal {M}}$$
M
, respectively.
Publisher
Springer Science and Business Media LLC
Subject
Applied Mathematics,Mathematics (miscellaneous)
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