In this paper we will present the pointwise and normwise estimations of the deviations considered by W. Łenski, B. Szal, [Acta Comment. Univ. Tartu. Math., 2009, 13, 11-24] and S. Saini, U. Singh, [Boll. Unione Mat. Ital., 2016, 9, 495-504] under general assumptions on the class considered sequences defining the method of the summability. We show that the obtained estimations are the best possible for some subclasses of Lp by constructing the suitable type of functions.

We consider the pointwise and normwise approximation of function by some special matrix means of its Fourier series. The results corresponding to the theorem of Łenski and Szal in [5] and the results of Saini and Singh in [6] are shown. Some special cases as corollaries are also formulated. 2010 Mathematics Subject Classification: 42A24.