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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 polar derivative of a constrained polynomial
In this paper, we establish several new inequalities of Bernstein and Turán-type that relate the uniform norm of the polar derivative and the polynomial. The obtained results produce various inequalities that ...
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Article
Extremal problems of Turán-type for a univariate complex coefficient polynomial
In this paper, we establish some new inequalities in the plane that are inspired by some classical Turán-type inequalities that relate the norm of a univariate complex coefficient polynomial and its derivative...
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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 Erdös–Lax-type for a complex polynomial
If P(z) is a polynomial of degree n which does not vanish in \(|z|<k,\,k\le 1\) | ...
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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
Integral-norm estimates for the polar derivative of a polynomial
In this paper, we establish some integral-norm estimates for lacunary-type polynomials in the complex plane that are inspired by some classical Bernstein-type inequalities that relate the sup-norm of a polynom...
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Article
Generalizations of some inequalities for rational functions with prescribed poles and restricted zeros
The main purpose of this paper is to established the modulus of derivative of rational functions r(z) having all its zeros in $$|z|\le k \le 1...
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Article
A note on an inequality of Paul Turán concerning polynomials
If \(P(z):=\sum \nolimits _{v=0}^{n}a_vz^v\) P ...
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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
Inequalities concerning polynomials in the complex domain
In this paper, we prove some inequalities that relate the sup-norm of a univariate complex coefficient polynomial and its derivative, when there is a restriction on its zeros. We further obtain the polar deriv...
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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...
