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Bernstein Type
Inequalities for
Composite
Polynomials
Bashir Ahmad Zargar (1) and Shabir Ahmad Malik
(2)
(1) Department
of Mathematics,
University of
Kashmir,
Srinagar-
190006, India
Email address:
bazargar@gmail.com
(2) Department of
Mathematics,
University of
Kashmir, Srinagar-
190006, India
Email address:
shabir2101@gmail.com
Doi :
https://doi.org/10.47013/15.4.22
Cited by :
Jordan J. Math &
Stat.,
15 (4B) (2022),
1127 - 1135
PDF
Received on:
Nov. 7, 2021;
Accepted
on: Jan. 30,
2022
Abstract. Establishing
the lower and
upper bound
estimates for
the maximum
modulus of the
derivative of
composition of
polynomials
p(q(z)), where
q(z) is a
polynomial of
degree m is an
intriguing
problem in
geometric theory
of polynomials.
In this paper,
the maximum
modulus for
composite
polynomials of
Bernstein type
is taken up with
constraints such
as the given
polynomial does
not vanish in
the disc |z| <
k, where k ≥ 1
which in
particular
yields some
known
inequalities of
this type as
special cases.
In addition, the
case when all
the zeros of the
underlying
polynomial lie
in |z| ≤ k,
where k ≤ 1 is
also considered.
Keywords: Bernstein’s
inequality,
Polynomial,
Zeros,
Composition of
polynomials.
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