7 Result(s)
within
Abdullah Mir
Numerical Analysis
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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
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
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
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
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
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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Article
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...
