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Trigonometric approximation in $L_{p}$-norm. (English) Zbl 1057.42004
Summary: We weaken the conditions of monotonicity given by {\it P. Chandra} [J. Math. Anal. Appl. 275, No. 1, 13--26 (2002; Zbl 1011.42001)], where he investigated trigonometric polynomials associated with $f \in \text{Lip}(\alpha,p)$ $(0<\alpha \leqslant 1, p \geqslant 1)$ to approximate $f$ in $L_p$-norm to the degree of $O(n^{-\alpha}) (0<\alpha \leqslant 1)$.

42A10Trigonometric approximation
Full Text: DOI
[1] Chandra, P.: A note on degree of approximation by nörlund and Riesz operators. Mat. vestnik 42, 9-10 (1990) · Zbl 0725.42004
[2] Chandra, P.: Trigonometric approximation of functions in lp-norm. J. math. Anal. appl. 275, 13-26 (2002) · Zbl 1011.42001
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[6] Mohapatra, R. N.; Russell, D. C.: Some direct and inverse theorems in approximation of functions. J. austral. Math. soc. Ser. A 34, 143-154 (1983) · Zbl 0518.42013
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