Results 1 to 10 of about 2,053,807 (187)
Inequalities for the Polar Derivative of a Polynomial [PDF]
Journal of Inequalities and Applications, 2009 Let p(z) be a polynomial of degree n and for any real or complex number α, and let Dαp(z)=np(z)+(α−z)p′(z) denote the polar derivative of the polynomial p(z) with respect to α.
M. Bidkham +2 more
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University of Aden Journal of Natural and Applied Sciences, 2023 In this paper, certain new results concerning the maximum modulus of the polar derivative and the generalized polar derivative of a polynomial with restricted zeros are obtained. These estimates strengthen some well known inequalities for polynomial
Adeeb Tawfik Hasson Al-Saeedi +1 more
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Estimates for the polar derivative of a constrained polynomial on a disk
Cubo, 2022 This work is a part of a recent wave of studies on inequalities which relate the uniform-norm of a univariate complex coefficient polynomial to its derivative on the unit disk in the plane.
Gradimir V. Milovanović +2 more
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Inequalities for the Polar Derivative of a Polynomial [PDF]
Abstract and Applied Analysis, 2012 For a polynomial 𝑝(𝑧) of degree 𝑛, we consider an operator 𝐷𝛼 which map a polynomial 𝑝(𝑧) into 𝐷𝛼𝑝(𝑧)∶=(𝛼−𝑧)𝑝′(𝑧)+𝑛𝑝(𝑧) with respect to 𝛼. It was proved by Liman et al. (2010) that if 𝑝(𝑧) has no zeros in |𝑧|
Ahmad Zireh
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Lγ Inequalities for the Polar Derivative of Polynomials
Malaysian Journal of Mathematical Sciences, 2023 In this paper, firstly, we obtain an inequality in Lγ analogue concerning the polar derivative for a polynomial p(ξ) = Xm ν=0 cνξν of degree m having no zero in |ξ| < r, r ≥ 1 proved by Govil et al. [15].
M. S. Singh +3 more
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Some Bounds for the Polar Derivative of a Polynomial [PDF]
International Journal of Mathematics and Mathematical Sciences, 2018 The polar derivative of a polynomial p(z) of degree n with respect to a complex number α is a polynomial np(z)+α-zp′(z), denoted by Dαp(z). Let 1≤R≤k. For a polynomial p(z) of degree n having all its zeros in z≤k, we investigate a lower bound of modulus ...
Jiraphorn Somsuwan +1 more
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Inequalities for the Polar Derivative of A Polynomial [PDF]
Mathematics and Statistics, 2013 IfP (z) = anz n + n P v= a n vz n v , 1 n, has all its zeros onjzj = k, k 1, then it was recently proved by Dewan and Ahuja (3) that for every real or complex number withj j k.
M. S. Pukhta
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On Polynomials and Their Polar Derivative
Mathematical Sciences and Applications E-Notes, 2016 Let P (z) be a polynomial of degree n and for any complex number α, let DαP (z) = nP (z) + (α− z)P ′(z) denote the polar derivative of P (z) with respect to α.
A. Mir
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New antifungal and less toxic zwitterionic derivatives of 26-membered polyene antibiotic – pimaricin containing N-benzyl and N-alkyl moieties and their molecular mechanism [PDF]
Journal of Enzyme Inhibition and Medicinal ChemistryN-derivatives of pimaricin (PIM) were synthesised as zwitterions or in a non-ionic form, influencing water solubility and toxicity in normal cells (HDF).
Ewelina Smolarz +8 more
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On extremal properties for the polar derivative of polynomials
Analysis in Theory and Applications, 2011 Summary: If \(p(z)\) is a polynomial of degree \(n\) having all its zeros on \(|z|=k\), \(k\leq 1\), then it is known that \[ \max\limits_{|z|=1}|p'(z)|\leq \frac n {k^{n-1}+k^n}\max\limits_{|z|=1}|p(z)|. \] In this paper, we generalize the above inequality by extending it to the polar derivative of a polynomial of the type \(p(z)=c_nz^n +\sum\limits ...
K. K. Dewan, Arty Ahuja
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