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Bernstein-type inequalities for a polynomial not vanishing in a disk
We establish some Bernstein-type inequalities which are point-wise estimates for the modulus of the derivative and polar derivative of a polynomial....
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On the reduced Bernstein-Sato polynomial of Thom-Sebastiani singularities
Given two holomorphic functions f and g defined in two respective germs of complex analytic manifolds ( X , x ) and ( Y , y ), we know thanks to M. Saito...
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Numerical Solutions of High-Order Differential Equations with Polynomial Coefficients Using a Bernstein Polynomial Basis
The paper presents a novel method that allows one to establish numerical solutions of linear and nonlinear ordinary differential equations—with...
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On Bernstein Inequality via Chebyshev Polynomial
Motivated by applications to the Carleson embedding theorem with matrix weights, Culiuc and Treil proved a Bernstein-type inequality for complex...
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Bernstein Polynomial Approximation of Fixation Probability in Finite Population Evolutionary Games
We use the Bernstein polynomials of degree d as the basis for constructing a uniform approximation to the rate of evolution (related to the fixation...
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Bounds-constrained polynomial approximation using the Bernstein basis
A fundamental problem in numerical analysis and approximation theory is approximating smooth functions by polynomials. A much harder version under...
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Extension of Some Bernstein-Type Inequalities to the Polar Derivative of a Polynomial
In this paper, we present new findings regarding the upper bound estimates for the polar derivative of a polynomial on the unit disk. We take into...
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On the Randomized Bernstein Approximation Theorem and the Order of Approximation
AbstractThe Weierstrass Approximation Theorem provides an important result by approximating a given continuous function defined on a closed interval...
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Bernstein–Jacobi-type operators preserving derivatives
A general frame for Bernstein-type operators that preserve derivatives is given. We introduce Bernstein-type operators based in the weighted...
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On the eigenfunctions of the q-Bernstein operators
The eigenvalue problems for linear operators emerge in various practical applications in physics and engineering. This paper deals with the...
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Bernstein-Type Operators on the Unit Disk
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study...
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Generalized Markov–Bernstein Inequalities and Stability of Dynamical Systems
AbstractWe analyze the Markov–Bernstein type inequalities between the norms of functions and of their derivatives for complex exponential...
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Operator Preserving Bernstein-Type Inequalities between Polynomials
AbstractIn this paper, we establish some operator preserving inequalities of Bernstein-type in the uniform-norm between univariate complex...
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Bernstein and Turán-type inequalities for a polynomial with constraints on its zeros
This paper considers the well known Bernstein and Turán-type inequalities that relate the uniform norm of a polynomial to that of its derivative on...
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Bernstein Eigenvarieties
We construct parabolic analogues of (global) eigenvarieties, of patched eigenvarieties and of (local) trianguline varieties, that we call,...
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Bernstein–Riemann Interpolation Formula for Arbitrary Continuous Functions on an Interval
AbstractFor arbitrary continuous functions on the interval [0, 1], we obtain an interpolation formula based on known values of these functions on...
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Bernstein Collocation Method for Solving High-Order Singular Differential–Difference Equations
The purpose of this article is to present an efficient numerical approach based on Bernstein polynomials for solving high-order linear singular...
