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Article
On the number of zeros of a polynomial in a disk
The prime concern of this paper is to obtain bounds concerning the number of zeros of polynomials in a specific region. In this paper, we use a new technique which overcome the short-comings of previous known ...
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Article
Annular regions containing all the zeros of a polynomial
A result due to Tôya, Montel and Kuniyeda concerning the location of the zeros of a polynomial states that if $$P(z)=a_{n}z^n+a_{n-1}z^{n-1}+a_{n-2}z^...
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Article
Certain Bernstein-type \(L_p\) inequalities for polynomials
Let P(z) be a polynomial of degree n, then it is known that for \(\alpha \in {\mathbb {C}}\) ...
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Article
Inequalities for Rational Functions with Prescribed Poles
For rational functions \(R(z)=P(z)/W(z)\) , where ...
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Article
Sharpening of Erdős–Lax Inequality for Polynomials
In this paper, we establish results concerning the upper bound estimates for the maximum modulus of the derivative of a polynomial on the unit disk. Our results are the complement to the work recently presente...
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Article
Zygmund-Type Integral Inequalities for Complex Polynomials
Let \({\mathcal {P}}_n\) P n ...
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Article
Integral Inequalities for the Growth and Higher Derivative of Polynomials
Let \(P(z)\) be a polynomial of degree
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Article
On Visser’s Inequality Concerning an Estimation of Polynomial Coefficients
If P(z) = \(\sum\nolimits_{j = 0}^n {{{a}_{j}}{{z}^{j}}} \) is an nth degree polynomial that has n...
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Article
On the zeros of a class of generalized derivatives
In this paper, we obtain some results concerning the zeros of a class of generalized derivatives which are analogous to those for the ordinary derivative and the polar derivatives of polynomials.
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Article
Some inequalities for polynomials with restricted zeros
By using the boundary Schwarz lemma, it was shown by Dubinin (J Math Sci 143:3069–3076, 2007) that if P(z) is a polynomial of degree n having all its zeros in
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Article
On the zeros of certain composite polynomials and an operator preserving inequalities
If all the zeros of nth degree polynomials f(z) and \(g(z) = \sum _{k=0}^{n}\lambda _k\left( {\begin{array}{c}n\\ k\end{array}}\right) z^k\) ...
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Article
On a refinement of Turán’s inequality
In this paper, we shall obtain some inequalities for the polar derivative of polynomial having all zeros in \(|z|\le k, k \ge 1.\) ...
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Article
On a Composition Preserving Inequalities between Polynomials
The Schur-Szegö composition of two polynomials \(f\left( z \right) = \sum\nolimits_{j = 0}^n {{A_j}{z^j}} \) ...
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Article
Inequalities Concerning the Polar Derivative of a Polynomial
In this paper, certain refinements and generalizations of some inequalities concerning the polynomials and their polar derivative are obtained.
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Article
Bounds for the zeros of complex-coefficient polynomials
In this paper, we present certain results on the bounds for the moduli of the zeros of a polynomial with complex coefficients which among other things contain some generalizations and refinements of classical ...
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Article
L p inequalities for the Schur–Szegő composition of polynomials
Certain sharp L p inequalities concerning the Schur–Szegő composition of polynomials, which among other things include classical Bernstein-type inequali...
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Article
On an inequality concerning the polar derivative of a polynomial
In this paper, we present a correct proof of an L p -inequality concerning the polar derivative of a polynomial with restricted zeros. We also extend Zyg...
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Chapter
On an Inequality of S. Bernstein and the Gauss-Lucas Theorem
In this paper we first present an interesting generalization of the Gauss-Lucas Theorem. Next we use this result as a basic tool to prove certain compact generalizations of the well-known inequalities of S. Be...
