Results 11 to 20 of about 2,567 (221)

On some inequalities for the two-parameter Mittag-Leffler function in the complex plane

Journal of Mathematical Analysis and Applications
For the two-parameter Mittag-Leffler function $E_{α,β}$ with $α> 0$ and $β\ge 0,$ we consider the question whether $|E_{α,β}(z)|$ and $E_{α,β}(\Re z)$ are comparable on the whole complex plane. We show that the inequality $|E_{α,β}(z)|\le E_{α,β}(\Re z)$ holds globally if and only if $E_{α,β}(-x)$ is completely monotone on $(0,\infty)$. For $α\in [1,
Stefan Gerhold, Roberto Garrappa, Marina Popolizio   +2 more
exaly   +5 more sources

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, Abdullah Mir, Adil Hussain   +2 more
doaj   +1 more source

INEQUALITIES FOR A CLASS OF MEROMORPHIC FUNCTIONS WHOSE ZEROS ARE WITHIN OR OUTSIDE A GIVEN DISK

Ural Mathematical Journal, 2023
In this paper, we consider a class of meromorphic functions \(r(z)\) having an \(s\)-fold zero at the origin and establish some inequalities of Bernstein and Turán type for the modulus of the derivative of rational functions  in the sup-norm on the disk ...
Mohd Yousf Mir, Shah Lubna Wali, Wali Mohammad Shah   +2 more
doaj   +1 more source

Inequalities for rational functions in the complex plane

Filomat, 2023
This paper investigates inequalities for rational functions with prescribed poles and zeros located inside or outside a disk of radius k. We extend classical polynomial inequalities due to Govil (1973, 1980) to the setting of rational functions. In particular, we establish a relationship between the maximum modulus of a rational function on the circle ...
openaire   +1 more source

Optimal control of satellite system model using Linear Matrix inequality approach

Results in Control and Optimization, 2023
In this paper, a robust control strategy has been proposed for the satellite attitude control system, namely, ℋ∞with regional pole constraints. This design method has been applied to eliminate the effects of disturbances and uncertainties, which are ...
Ali Khudhair Al-Jiboory
doaj   +1 more source

Equivalence of the Local Markov Inequality and a Kolmogorov Type Inequality in the Complex Plane [PDF]

Potential Analysis, 2012
Let \(m,\kappa\geq 1.\) A compact set \(E\subset\mathbb{C}\) is said to admit the local Markov property \(\mathrm{LMP}(m,\kappa)\) if, for all \( n\in\mathbb{N}\), \(z_0\in E\), \(r\in (0,1]\), the holomorphic polynomials \(P\) of degree at most \(n\) and \(j\in \mathbb{N}\) satisfy \[ |P^{(j)}(z_0)|\leq\left(\frac{c_1n^{\kappa}}{r^m}\right)^j\| P\|_{E\
Białas-Cież, Leokadia, Eggink, Raimondo   +1 more
openaire   +3 more sources

Study on new integral operators defined using confluent hypergeometric function

Advances in Difference Equations, 2021
Two new integral operators are defined in this paper using the classical Bernardi and Libera integral operators and the confluent (or Kummer) hypergeometric function.
Georgia Irina Oros
doaj   +1 more source

Prabhakar Functions of Le Roy Type: Inequalities and Asymptotic Formulae

Mathematics, 2023
In this paper, the four-index generalization of the classical Le Roy function is considered on a wider set of parameters and its order and type are given.
Jordanka Paneva-Konovska
doaj   +1 more source

Applications of Inequalities in the Complex Plane Associated with Confluent Hypergeometric Function [PDF]

Symmetry, 2021
The idea of inequality has been extended from the real plane to the complex plane through the notion of subordination introduced by Professors Miller and Mocanu in two papers published in 1978 and 1981. With this notion came a whole new theory called the theory of differential subordination or admissible functions theory.
openaire   +1 more source

Pole Assignment for Active Vibration Control of Linear Vibrating Systems through Linear Matrix Inequalities

Applied Sciences, 2020
This paper proposes a novel method for pole placement in linear vibrating systems through state feedback and rank-one control. Rather than assigning all the poles to the desired locations of the complex plane, the proposed method exactly assigns just the
Roberto Belotti, Dario Richiedei, Iacopo Tamellin, Alberto Trevisani   +3 more
doaj   +1 more source