ON ZYGMUND–TYPE INEQUALITIES CONCERNING POLAR DERIVATIVE OF POLYNOMIALS [PDF]
Ural Mathematical Journal, 2021 Let \(P(z)\) be a polynomial of degree \(n\), then concerning the estimate for maximum of \(|P'(z)|\) on the unit circle, it was proved by S. Bernstein that \(\| P'\|_{\infty}\leq n\| P\|_{\infty}\).
Nisar Ahmad Rather +2 more
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Estimates for the polar derivative of a constrained polynomial on a disk [PDF]
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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Integral mean estimates of Turán-type inequalities for the polar derivative of a polynomial with restricted zeros [PDF]
Open MathematicsIn this article, we extend inequalities concerning the polar derivative of a polynomial to integral mean for the class of polynomials with s-fold zero at the origin and the remaining zeros inside some closed disk of radius kk for k≥1k\ge 1 and k≤1k\le 1,
Singha Nirmal Kumar, Chanam Barchand
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INTEGRAL ANALOGUE OF TURÁN-TYPE INEQUALITIES CONCERNING THE POLAR DERIVATIVE OF A POLYNOMIAL [PDF]
Ural Mathematical JournalIf \(w(\zeta)\) is a polynomial of degree $n$ with all its zeros in \(|\zeta|\leq \Delta, \Delta\geq 1\) and any real \(\gamma\geq 1\), Aziz proved the integral inequality [1] $$ \left\lbrace\int_{0}^{2\pi}\left|1+\Delta^ne^{i\theta}\right|^{\gamma}d ...
Mayanglambam Singhajit Singh +1 more
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Valiron’s Interpolation Formula and a Derivative Sampling Formula in the Mellin Setting Acquired via Polar-Analytic Functions [PDF]
, 2023 In this paper, we first recall some recent results on polar-analytic functions. Then we establish Mellin analogues of a classical interpolation of Valiron and of a derivative sampling formula. As consequences a new differentiation formula and an identity
Mantellini, Ilaria +3 more
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Lp-inequalities for the polar derivative of a lacunary-type polynomial [PDF]
, 2021 In this paper, we extend an inequality concerning the polar derivative of a polynomial in Lp-norm to the class of lacunary polynomials and thereby obtain a bound that depends on some of the coefficients of the polynomial as ...
Gulzar, Suhail +2 more
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Inequalities concerning the rate of growth of polynomials involving the polar derivative [PDF]
, 2020 This paper contains some results for algebraic polynomials in the complex plane involving the polar derivative that are inspired by some classical results of Bernstein.
Mir, Abdullah, Malik, Adil Hussain
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Polynomials with polar derivatives [PDF]
Functiones et Approximatio Commentarii Mathematici, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mir, Abdullah, Wani, Ajaz
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Search for Non-Protein Protease Inhibitors Constituted with an Indole and Acetylene Core
Molecules, 2021 A possible inhibitor of proteases, which contains an indole core and an aromatic polar acetylene, was designed and synthesized. This indole derivative has a molecular architecture kindred to biologically relevant species and was obtained through five ...
Marco A. Almaraz-Girón +7 more
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Synthesis, spectroscopy, and photophysical properties of newly magnesium (II) phthalocyanine
MANAS: Journal of Engineering, 2021 2(3),9(10),16(17),23(24)-tetrakis-2,6-dimethoxyphenoxy substituted magnesium (II) phthalocyanine, which has very good solubility in polar and non-polar solvents and does not aggregate, was synthesized.
Mehmet Pişkin +2 more
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