Estimates of Approximation by Kantorovich Type Operators in Terms of the Second Modulus of Continuity

Abstract

We study approximation of bounded measurable functions on the segment [0, 1] by Kantorovich type operators $$ {B}_n=\sum \limits_{j=0}^n{C}_n^j{x}^j{\left(1-x\right)}^{n-j}{F}_{n,j}, $$ where Fn, j are functionals generated by various probability measures with sufficiently small supports. The error of approximation is estimated in terms of the second modulus of continuity. The estimate is sharp.