Geodesic
Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin
Daghestan Electronic Mathematical Reports, no. 8 (2017), pp. 70-92

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On the basis of trigonometric sums of Fourier $S_n(f,x)$ and classical means of Valle Poussin $$ _1V_{n,m}(f,x)= \frac1n\sum_{l=m}^{m+n-1}S_l(f,x) $$ in this paper, repeated mean Valle Poussin is introduced as follows $$ _2V_{n,m}(f,x)= \frac1n\sum_{k=m}^{m+n-1}{}_1V_{n,k}(f,x), $$ $$ {}_{l+1}V_{n,m}(f,x)= \frac1n\sum_{k=m}^{m+n-1} {}_{l}V_{n,k}(f,x)\quad(l\ge1). $$ On the basis of the mean $_2V_{n,m}(f,x)$ and overlapping transforms, operators that approximate continuous (in general, nonperiodic) functions are constructed and their approximative properties are investigated.
Keywords: the repeated mean Valle Poussin, overlapping transforms, local approximative properties. 
I. I. Sharapudinov. Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin. Daghestan Electronic Mathematical Reports, no. 8 (2017), pp. 70-92. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a7/
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