Abstract

We prove two Grüss-type inequalities for positive linear operator approximation, i.e., inequalities explaining the non-multiplicativity of such mappings. Instead of the least concave majorant of the first order modulus of continuity, we employ second order moduli of smoothness and show in the case of the classical Bernstein operators that in certain cases this leads to better results than those obtained earlier.

Keywords: Grüss-type inequality; positive linear operators; Bernstein operator; variation-diminishing Schoenberg-splines; second order modulus of smoothness.

MSC: 41A36, 41A17, 41A25, 39B62

Pages:  247$-$252     

Volume  63 ,  Issue  3 ,  2011