This paper considers the well known Bernstein and Turán-type inequalities that relate the
uniform norm of a polynomial to that of its derivative on the unit circle in the plane. Here, we …

Let p (z) be a polynomial of degree n having no zero in| z|< k, k≤ 1, then Govil proved
$$\max_ {{\mid} z {\mid}= 1}{\mid} p^{\prime}(z){\mid}{\leq}{\frac {n}{1+ k^ n}}\max_ {{\mid} z …

This work is a part of a recent wave of studies on inequalities which relate the uniform-norm
of a univariate complex coefficient polynomial to its derivative on the unit disk in the plane …

Let p (z) be a polynomial of degree n having no zero in| z|< k, k≤ 1, then Govil [Proc. Nat.
Acad. Sci., 50 (1980), 50-52] proved max| z|= 1| p′(z)|≤ n 1+ kn max| z|= 1| p (z)|, provided …

In this paper we introduce an operator that can be thought as a derivative of variable order,
ie the order of the derivative is a function. We prove several properties of this operator, for …

In this paper, we prove certain sharp inequalities that relate the uniform norm of the
derivative and the polynomial itself, in case when the zeros are outside or inside some …

If P (z) is a polynomial of degree n having no zeros in| z|< 1, then Erdös conjectured and
later Lax (Bull. Amer. Math. Soc. 50 (1944) 509-513) proved that max| z|= 1| P′(z)|≤ n 2 …

The well-known Erdos-Lax and Turan-type inequalities, which relate the uniform norm of a
univariate complex coefficient polynomial to its derivative on the unit circle in the plane, are …

In this work we prove some new Bernstein-type inequalities for the polynomials with
restricted zeros. Our results strengthen some recently proved Erdős–Lax and Turán-type …

In this paper, we establish some generalizations of the upper bound estimates for the
modulus of the derivative of a polynomial on the unit disk while accounting for the …