Sur la suite des opérateurs Bernstein composés (On the sequence of composite Bernstein operators)

Abstract

We consider a sequence of composite Bernstein operators and the quadrature formulae associated with them. Upper bounds for the approximation error of continuous functions and for the approximation of integrals of continuous functions are given. The bounds are described in terms of moduli of continuity of order one and two. Two inequalities of Tchebycheff-Grüss-type are also included.

Keywords

• composite Bernstein operators
• composite quadrature formulas
• modulus of continuity
• degree of approximation
• inequalities of Chebyshev-Grüss type