Results 1 to 10 of about 2,468 (122)
Finite-infinite range inequalities in the complex plane [PDF]
International Journal of Mathematics and Mathematical Sciences, 1991 Let E⫅C be closed, ω be a suitable weight function on E, σ be a positive Borel measure on E. We discuss the conditions on ω and σ which ensure the existence of a fixed compact subset K of E with the following property.
H. N. Mhaskar
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Weighted polynomial inequalities in the complex plane
Journal of Approximation Theory, 2012 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Vladimir V Andrievskii
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Differential subordinations and inequalities in the complex plane
Journal of Differential Equations, 1987 Let f and F be analytic in the unit disc U. The function f is subordinate to F, written \(f\prec F\) or f(z)\(\prec F(z)\), if F is univalent, \(f(0)=F(0)\) and f(U)\(\subset F(U)\). The authors deal with second order differential subordinations of the form \((1)\quad \psi (p(z),zp'(z),z^ 2p''(z);z)\prec h(z),\) where \(\psi\) : \({\mathbb{C}}^ 3\times
Sanford Miller, Petru T Mocanu
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Second order differential inequalities in the complex plane
Journal of Mathematical Analysis and Applications, 1978 AbstractLet w(z) be regular in the unit disk U and let h(r, s, t) be a complex function defined in a domain of C3. The authors determine conditions on h such that ¦ h(w(z), zw′(z), z2w″(z))¦ < 1 implies ¦ w(z)¦ < 1 and such that Re h(w(z), zw′(z), z2w″(z)) > 0 implies Re w(z) > 0. Applications of these results to univalent function theory, differential
Sanford Miller, Petru T Mocanu
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Hilbert transform in the complex plane and area inequalities for certain quadratic differentials. [PDF]
Michigan Mathematical Journal, 1987 The author studies the Hilbert transform \[ T_ E(z)=- \frac{1}{\pi}\iint_{B}\frac{\chi_ E(\zeta)d\mu (\zeta)}{(z-\zeta)^ 2}, \] where \(\chi_ E\) is the characteristic function of a measurable set E in the (open) unit disk B and \(d\mu\) (\(\zeta)\) is Lebesgue measure.
Tadeusz Iwaniec
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Some Inequalities on Polynomials in the Complex Plane Concerning a Linear Differential Operator
Journal of MathematicsIn this paper, we consider new extremal problems in the uniform norm between a univariate complex polynomial and its associated reciprocal polynomial involving a generalized B-operator.
Mayanglambam Singhajit Singh +2 more
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Uniform and pointwise Bernstein-Walsh-type inequalities on a quasidisk in the complex plane [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2016 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Abdullayev, F.G., Özkartepe, P.
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AIMS Mathematics, 2021 <abstract><p>The results presented in this paper highlight the property of the Gaussian hypergeometric function to be a Carathéodory function and refer to certain differential inequalities interpreted in form of inclusion relations for subsets of the complex plane using the means of the theory of differential superordination and the method ...
Georgia Irina Oros
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Turkish Journal of Mathematics, 2022 In this paper, we study Bernstein-Walsh-type estimates for the derivatives of an arbitrary algebraic polynomial on some general regions of the complex plane.
Fahreddin Abdullayev
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Inequalities Involving Weighted Means in a Disc of the Complex Plane
Journal of Mathematical Analysis and Applications, 2000 For complex numbers \(z_j\), \(j=1,2,\dots,n\), such that \(|z_j-1|\leq r\), \(r\in(0,1)\), the author considers the weighted means: \(H:= (\sum^n_{j=1} \lambda_jz_j^{-1})\), \(G:=\prod^n_{j=1} z_j^{\lambda_j}\) and \(A: =\sum^n_{j=1} \lambda_jz_j\), where \(\lambda_j>0\), \(\lambda_1+ \cdots+ \lambda_n =1\). Among other results, he proves: Theorem 1. \
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