Abstract
We consider the strong means of Fourier series generated by infinite nonnegative triangular matrices and prove some estimates of such means in the case of a matrix with rows stating the sequences from the class GM(5β). Our theorems correspond to the results of L. Leindler [L. Leindler, A note on strong approximation of Fourier series, Anal. Math. 29 (2003) 195–199] and essentially extend the result of S.M. Mazhar and V. Totik [S.M. Mazhar, V. Totik, Approximation of continuous functions by T -means of Fourier series, J. Approx. Theory, 60 (1990) 174–182].
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