Degree of approximation to functions in a normed space. (English) Zbl 0945.42001

Let \(A\) be a lower triangular nonnegative matrix and let \(\{t_n\}\) be the sequence of \(A\)-transforms of the sequence of partial sums of the Fourier series of a \(2\pi\)-periodic function \(f\). Here, the authors study the degree of approximation of \(f\) in the Hölder metric by the sequence \(\{t_n\}\). The theorems proved in this paper generalize some existing results in the field.


42A10 Trigonometric approximation
41A25 Rate of convergence, degree of approximation
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