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

Mittal, M. L.; Rhoades, B. E.

J. Comput. Anal. Appl. 2, No. 1, 1-10 (2000).

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.

Reviewer: Ganesh Datta Dikshit (Auckland)

MSC:

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

Keywords:

matrix transform; Fourier series; degree of approximation; Hölder metric