On moduli of smoothness and averaged differences of fractional order
arXiv:1709.03168 · doi:10.1515/fca-2017-0051
Abstract
We consider two types of fractional integral moduli of smoothness, which are widely used in theory of functions and approximation theory. In particular, we obtain new equivalences between these moduli of smoothness and the classical moduli of smoothness. It turns out that for fractional integral moduli of smoothness some pathological effects arise.