  We will present an estimation of the $H_{k_{0},k_{r}}^{q}f$ $\ $and $%
H_{u}^{\lambda \varphi}f$ means as a approximation versions \ of \ the Totik
type generalization$(\text{see \cite{11, 12}}) $ \ of the results of \ J.
Marcinkiewicz and A. Zygmund in \cite{JM, ZA}. As a measure of such
approximations we will use the function constructed on the base of definition
of the Gabisonia points \cite{1}. Some results on the norm approximation will
also given.
