Abstract
We will present an estimation of the generalized strong mean left( H,Phi right) 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 complementary to Phi on the base of definition of the Gabisoniya points. Some corollary and remark will also be given.
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