An application of a method of summability to Fourier series
Abstract
Applying
-repeated de la Vallée Poussin sums, we have proved four theorems which show the upper bound of the
-repeated de la Vall'ee Poussin kernel, their convergence at a point, the deviation between a continuous function and the
-repeated de la Vallée Poussin sums of partial sums of its Fourier series, and finally we determine the degree of approximation of functions belonging to ordinary Lipschitz class.
![r](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/4b43b0aee35624cd95b910189b3dc231.png)
![r](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/4b43b0aee35624cd95b910189b3dc231.png)
![r](http://siba-ese.unisalento.it/plugins/generic/latexRender/cache/4b43b0aee35624cd95b910189b3dc231.png)
Keywords:
Fourier series; de la Vallée Poussin sums; Lipschitz class; modulus of continuity; the best approximation
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