Geodesic
Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin
Daghestan Electronic Mathematical Reports, Tome 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. 
@article{DEMR_2017_8_a7,
     author = {I. I. Sharapudinov},
     title = {Overlapping transformations for approximation of continuous functions by means of repeated mean {Valle} {Poussin}},
     journal = {Daghestan Electronic Mathematical Reports},
     pages = {70--92},
     publisher = {mathdoc},
     volume = {8},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DEMR_2017_8_a7/}
}
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I. I. Sharapudinov. Overlapping transformations for approximation of continuous functions by means of repeated mean Valle Poussin. Daghestan Electronic Mathematical Reports, Tome 8 (2017), pp. 70-92. http://geodesic.mathdoc.fr/item/DEMR_2017_8_a7/