A characterization of weighted approximations by the Post-Widder and the Gamma operators

The weighted approximation errors of the Post-Widder and the Gamma operators are characterized for functions in with a weight xγ, γ∈R. Direct and strong converse theorems are proved. Two types of characteristics are used—weighted K-functionals of the approximated function itself and the classical fixed step moduli of smoothness taken on a simple modification of it.