Dimiter Dryanov

Bound-Preserving Operators and Bernstein Type Inequalities

Let D be the unit disk in the complex plane ℂ and

Multivariate Bernoulli Functions and Polyharmonically Exact Cubature Formula of Euler–Maclaurin

\Vert p\Vert:=\max_{z \in \partial {\rm D}}\mid p(z)\mid

Quadrature formulae with free nodes for periodic functions

, where

Bound preserving operators over classes of polynomials

p(z)=\sum_{k=0}^{n}a_k(p)z^k

On Certain Mean Values of Polynomials on the Unit Interval

is a polynomial of degree at most n and ak(p) ∈ ℂ;. The following sharpening of Bernstein’s inequality

On an improvement of Bernstein's polynomial inequalities

\Vert p^{\prime}\Vert+{2n\over n+2}\mid a_0(p)\mid \le n \Vert p\Vert