LAUSR

We will present an estimation of the generalized strong mean $$\left( H,\Phi \right) $$H,Φ as an approximation version of the Totik type generalization of the results of J. Marcinkiewicz and A. Zygmund on strong summability of Fourier series of integrable functions. As a measure of such approximation we will use the function constructed by function $$\Psi $$Ψ complementary to $$ \Phi $$Φ on the base of definition of the Gabisoniya points. Some corollary and remark will also be given.