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Open AccessOn the derivative and maximum modulus of a polynomial
If is a polynomial of degree , having all its zeros in
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Inequalities concerning to polar derivative of polynomials
Let P(z) be a polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1. In this paper, we shall generalize a result of Dewan et al. [3] to the polar derivative of a polynomial which in turn provides an impro...
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Some inequalities concerning polar derivative of a polynomial. Addendum
Let P(z) be s polynomial of degree n having all its zeros in |z| ≤ k, k ≥ 1. In this paper, we shall generalize a result of Aziz and Rather [2] which in turn provides an improvement of a recent result of Dewan et...
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Article
Some integral inequalities for the polar derivative of a polynomial
If P(z) is a polynomial of degree n which does not vanish in |z| < 1, then it is recently proved by Rather [Jour. Ineq. Pure and Appl. Math., 9 (2008), Issue 4, Art. 103] that for every γ> 0 and every real or com...
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Article
On an inequality of Paul Turan concerning polynomials
Let P(z) be a polynomial of degree n and P s (z) be its sth derivative. In this paper, we shall prove some inequalities for the sth derivative of...
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Article
Inequalities concerning the rate of growth of Polynomials
Let \(P(z)=a_{0}+\sum _{\nu =\mu }^{n}a_{\nu }z^{\nu },~1\le \mu \le n,\) ...
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Inequalities concerning rational functions with prescribed poles
In this paper, we establish some inequalities for rational functions with prescribed poles which generalize and refine the results of Li, Mohapatra and Rodriguez, Aziz and Shah, Qasim and Liman and others. A r...
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Article
On some inequalities concerning growth and derivatives of a polynomial
A well known result due to Ankeny and Rivlin states that if \(P(z)=\sum \nolimits _{\nu =0}^{n}a_{\nu }z^{\nu }\) ...
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Bernstein-Type Integral Inequalities for a Certain Class of Polynomials
In this paper, we establish some Bernstein-type integral inequalities for a certain class of polynomials involving the polar derivative. Our results generalize some known polynomial inequalities and include as...
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Article
Some sharp upper bound estimates for the maximal modulus of polar derivative of a polynomial
In this paper, we establish some sharp upper bound estimates for the maximal modulus of polar derivative of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk....
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A note on Ankeny–Rivlin theorem
In this paper, we consider the class of polynomials not vanishing in the unit disk and obtain a result that improves the results of Dubinin, Aziz and Dawood and the classical result of Ankeny and Rivlin.
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Article
Bernstein-type inequalities for certain class of meromorphic functions
In this paper, we shall obtain some Bernstein-type inequalities for certain class of meromorphic functions with restricted zeros and prescribed poles. Our results extend some well known polynomial inequalities...
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Article
Generalizations of Bernstein and Turán-Type Inequalities for the Polar Derivative of a Complex Polynomial
The goal of this paper is to extend to the polar derivatives some previous inequalities between the \(L^\gamma \)Lγ-norms of the derivative and of the polynomial itself, in case when the zeros are outside or insi...
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Some Inequalities for Rational Functions with Fixed Poles
By using lemmas of Dubinin and Osserman some results for rational functions with fixed poles and restricted zeros are proved. The obtained results strengthen some known results for rational functions and, in t...
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Article
Open AccessGeneralizations of Zygmund-type integral inequalities for the polar derivative of a complex polynomial
Some Zygmund-type integral inequalities for the polar derivatives of complex polynomials, inspired by the classical Bernstein-type inequalities that relate the uniform norms of polynomials and their derivative...
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Certain estimates of the derivative of a meromorphic function on boundary of the unit disk
In this paper we establish a family of comparison inequalities between rational functions with prescribed poles for the sup-norms on the unit circle in the complex plane. Certain estimates for the modulus of t...
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Article
Open AccessA Zygmund-type integral inequality for polynomials
Let P(z) be a polynomial of degree n which does not vanish in \(|z|<1\) | ...
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Article
Growth of a polynomial with restricted zeros
In this paper, we establish some upper bound estimates for the maximal modulus of a polynomial on a disk \(|z|=R, \,R\ge 1\) | z | = R , R ≥ 1 , when there is a restriction on its zeros. The obtained result...
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Article
Bernstein-Type Integral Inequalities for a Certain Class of Polynomials-II
In this paper, we establish some new inequalities in the plane that are inspired by some classical Bernstein-type inequalities that relate the sup-norm of a polynomial to that of its derivative on the unit cir...
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New Integral Norm Estimates of Bernstein-Type Inequalities for a Certain Class of Polynomials
In this paper, we establish some results on algebraic polynomials in the complex plane that are inspired by some classical Bernstein-type inequalities that relate the sup-norm of a polynomial to that of its de...
