On an Operator Preserving Inequalities Between Polynomials
Let P ( z ) be a polynomial of degree n. We consider an operator D α that maps P ( z ) into D α P ( z ) := nP ( z ) + (α − z ) P0 ( z ) and establish some results concerning the estimates of |D α P ( z ) | in the disk |z| = R ≥ 1 , and thereby obtain extensions and generalizations of numerous well-k...
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| Veröffentlicht in: | Ukrainian mathematical journal 2018, Vol.69 (8), p.1234-1247 |
|---|---|
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | eng |
| Schlagworte: | |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | Let
P
(
z
) be a polynomial of degree
n.
We consider an operator
D
α
that maps
P
(
z
) into
D
α
P
(
z
) :=
nP
(
z
) + (α
− z
)
P0
(
z
) and establish some results concerning the estimates of
|D
α
P
(
z
)
|
in the disk
|z|
=
R ≥
1
,
and thereby obtain extensions and generalizations of numerous well-known inequalities for polynomial. |
|---|---|
| ISSN: | 0041-5995 1573-9376 |
| DOI: | 10.1007/s11253-017-1427-2 |