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

We use the second modulus of continuity to estimate approximations a bounded measurable function on segment [0, 1] by Kantorovich type operators $$ {B}_n(f)(x)=\sum \limits_{j=0}^n{C}_n^j{x}^j{\left(1-x\right)}^{n-j}{F}_j(f), where Fj are functionals with sufficiently small supports and certain symmetry. The result obtained is sharp.