Geodesic
Methods of summation and best approximation
Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 11-20

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Let $\lambda=\{\lambda_k^n\}$ be a triangular method of summation, $f\in L_p$ $(1\le p\le\infty)$, $$ U_n(f,x,\lambda)=\frac{a_0}2+\sum_{k=1}^n\lambda_k^n(a_k\cos kx+b_k\sin kx). $$ Consideration is given to the problem of estimating the deviations $\|f-U_n(f,\lambda)\|_{L_p}$ in terms of aЁbest approximation $E_n(f)_{L_p}$ in abstract form (for a sequence of projectors in a Banach space). Various generalizations of known inequalities are obtained. 
@article{MZM_1968_4_1_a1,
     author = {L. P. Vlasov},
     title = {Methods of summation and best approximation},
     journal = {Matemati\v{c}eskie zametki},
     pages = {11--20},
     publisher = {mathdoc},
     volume = {4},
     number = {1},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a1/}
}
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L. P. Vlasov. Methods of summation and best approximation. Matematičeskie zametki, Tome 4 (1968) no. 1, pp. 11-20. http://geodesic.mathdoc.fr/item/MZM_1968_4_1_a1/