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Article
Estimation of Bounds for the Zeros of Polynomials and Regular Functions of a Quaternionic Variable
The estimation of zeros of a polynomial with quaternionic coefficients has been done by many mathematicians in the recent past using various approaches. In this paper, we estimate the upper bounds for the zero...
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Article
On zeros of the regular power series of a quaternionic variable
Using tools from the newly developed theory of regular functions and polynomials with quaternionic coefficients located on only one side of the variable, we derive zero-free regions for the related subclass of...
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Article
Bernstein-type inequalities for a polynomial not vanishing in a disk
We establish some Bernstein-type inequalities which are point-wise estimates for the modulus of the derivative and polar derivative of a polynomial. The obtained results produce various generalizations and ref...
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Article
On the zeros of a quaternionic polynomial: An extension of the Eneström-Kakeya theorem
We present some results on the location of zeros of regular polynomials of a quaternionic variable. We derive new bounds of Eneström-Kakeya type for the zeros of these polynomials by virtue of a maximum modulu...
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Article
Estimation of bounds for the zeros of polynomials and regular functions with quaternionic coefficients
The aim of this work is to consider bounds for the zeros of quaternionic polynomials and regular functions with coefficients located on only one side of the quaternionic variable. We will introduce several res...
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Article
A note on the Erdös-Lax inequality concerning polynomials
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 positioning of the zeros and extremal c...
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Article
Extremal Problems for a Polynomial and Its Polar Derivative
This paper considers the well known Erdős–Lax and Turán-type inequalities that relate the uniform norm of a univariate complex coefficient polynomial to that of its derivative on the unit circle in the plane. ...
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Article
Extension of Some Bernstein-Type Inequalities to the Polar Derivative of a Polynomial
In this paper, we present new findings regarding the upper bound estimates for the polar derivative of a polynomial on the unit disk. We take into consideration the positions of the zeros and extremal coeffici...
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Article
On the Erdös-Lax inequality and its various generalizations concerning polynomials
If P(z) is a polynomial of degree n having no zeros in \(|z|<1\) | ...
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Article
Zygmund-Type Integral Inequalities for Complex Polynomials
Let \({\mathcal {P}}_n\) P n ...
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Article
Inequalities of Turán-type for algebraic polynomials
In this paper, we establish some new inequalities in the complex plane that are inspired by some classical Turán-type inequalities that relate the norm of a univariate complex coefficient polynomial and its de...
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Article
A Turán-type inequality for polynomials
In this paper, we consider the class of polynomials \(P(z):=\sum \limits _{j=0}^{n}c_jz^j\) ...
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Article
Bernstein and Turán-type inequalities for a polynomial with constraints on its zeros
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 establish some new ine...
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Article
Comparison inequalities between rational functions with prescribed poles
Various versions of Bernstein and Turán-type inequalities are a classical topic in analysis. Over a period, these inequalities have been generalized for different classes of functions. Here, we establish some ...
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Article
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...
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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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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
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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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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Article
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...