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Some Inequalities for the Maximum Modulus of Rational Functions [PDF]

International Journal of Mathematics and Mathematical Sciences, 2021
For a polynomial pz of degree n, it follows from the maximum modulus theorem that maxz=R≥1pz≤Rnmaxz=1pz.
Robert Gardner, Narendra Kumar Govil, Prasanna Kumar   +2 more
doaj   +4 more sources

The Maximum Modulus Set of a Polynomial [PDF]

Computational Methods and Function Theory, 2021
AbstractWe study the maximum modulus set, $${{\mathcal {M}}}(p)$$ M ( p ) , of a polynomial p. We are interested in constructing p so that $${{\mathcal {M}}}(p)$$ M
Pardo-Simón, Leticia, Sixsmith, David J.   +1 more
openaire   +4 more sources

On the Maximum Modulus of Polynomials [PDF]

Proceedings of the American Mathematical Society, 1992
The maximum modulus on | z |
M. A. Qazi
openaire   +3 more sources

On the maximum modulus of a polynomial and its derivatives [PDF]

International Journal of Mathematics and Mathematical Sciences, 2005
Let f(z) be an arbitrary entire function and M(f,r)=max|z|=r|f(z)|. For a polynomial P(z), having no zeros in |z|
K. K. Dewan, Abdullah Mir
doaj   +2 more sources

Wiman’s Type Inequality in Multiple-Circular Domain

Axioms, 2021
In the paper we prove for the first time an analogue of the Wiman inequality in the class of analytic functions f∈A0p(G) in an arbitrary complete Reinhard domain G⊂Cp, p∈N represented by the power series of the form f(z)=f(z1,⋯,zp)=∑‖n‖=0+∞anzn with the ...
Andriy Kuryliak, Oleh Skaskiv
doaj   +1 more source

Generalized and Extended Versions of Ankeny–Rivlin and Improved, Generalized, and Extended Versions of Rivlin Type Inequalities for the s^th Derivative of a Polynomial

Mathematics, 2021
Let p(z) be a polynomial of degree n having no zeros in |z|
Kshetrimayum Krishnadas, Reingachan Ngamchui, Barchand Chanam   +2 more
doaj   +1 more source

Wiman's type inequality for analytic and entire functions and $h$-measure of an exceptional sets

Karpatsʹkì Matematičnì Publìkacìï, 2020
Let $\mathcal{E}_R$ be the class of analytic functions $f$ represented by power series of the form $f(z)=\sum\limits\limits_{n=0}^{+\infty}a_n z^n$ with the radius of convergence $R:=R(f)\in(0;+\infty].$ For $r\in [0, R)$ we denote the maximum modulus by
O.B. Skaskiv, A.O. Kuryliak
doaj   +1 more source

Growth estimates for a Dirichlet series and its derivative

Математичні Студії, 2020
Let $A\in(-\infty,+\infty]$, $\Phi$ be a continuous function on $[a,A)$ such that for every $x\in\mathbb{R}$ we have $x\sigma-\Phi(\sigma)\to-\infty$ as $\sigma\uparrow A$, $\widetilde{\Phi}(x)=\max\{x\sigma -\Phi(\sigma)\colon \sigma\in [a,A)\}$ be the ...
S.I. Fedynyak, P.V. Filevych
doaj   +1 more source

Vector-Valued Entire Functions of Several Variables: Some Local Properties

Axioms, 2022
The present paper is devoted to the properties of entire vector-valued functions of bounded L-index in join variables, where L:Cn→R+n is a positive continuous function.
Andriy Ivanovych Bandura, Tetyana Mykhailivna Salo, Oleh Bohdanovych Skaskiv   +2 more
doaj   +1 more source

Properties of power series of analytic in a bidisc functions of bounded $\mathbf{L}$-index in joint variables

Karpatsʹkì Matematičnì Publìkacìï, 2017
We generalized some criteria of boundedness of $\mathbf{L}$-index in joint variables for analytic in a bidisc functions, where $\mathbf{L}(z)=(l_1(z_1,z_2),$ $l_{2}(z_1,z_2)),$ $l_j:\mathbb{D}^2\to \mathbb{R}_+$ is a continuous function, $j\in\{1,2\},$
A.I. Bandura, N.V. Petrechko
doaj   +1 more source