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)
Reference15 articles.
1. Brown, J.E.: Successive coefficients of functions with positive real part. Int. J. Math. Anal. 4, 2491–2499 (2020)
2. Carlson, F.: Sur les coefficients d’une fonction bornée dans le cercle unité. Ark. Mat. Astr. Fys. 27A, 1–8 (1940)
3. Efraimidis, I.: A generalization of Livingston’s coefficient inequalities for functions with positive real part. J. Math. Anal. Appl. 435, 369–379 (2016)
4. Kowalczyk, B., Lecko, A., Sim, Y.J.: The sharp bound for the hankel determinant of the third kind for convex functions Bull. Aust. Math. Soc. 97, 435–445 (2018)
5. Kowalczyk, B., Lecko, A., Thomas, D.K.: The sharp bound of the third Hankel determinant for starlike functions Forum Math. 34, 1249–1254 (2022)
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