On the Approximation of Functions From Lp by Some Special Matrix Means of Fourier Series

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Abstract

The results corresponding to some theorems of S. Lal [Appl. Math. and Comput. 209 (2009), 346-350] and the results of W. Łenski and B. Szal [Banach Center Publ., 95, (2011), 339-351] are shown. The better degrees of pointwise approximation than these in mentioned papers by another assumptions on summability methods for considered functions are obtained. From presented pointwise results the estimation on norm approximation are derived. Some special cases as corollaries are also formulated.

[1] Lal S., Approximation of functions belonging to the generalized Lipschitz Class by C1 Np summability method of Fourier series, Applied Mathematics and Computation, 209(2009), 346-350.

[2] Leindler L., Integrability conditions pertaining to Orlicz space, J. Inequal. Pure and Appl. Math., 8(2)(2007), Art. 38, 6 pp.

[3] Lenski W., Szal B., Approximation of functions from Lp (ω)β by general linear operators of their Fourier series, Banach Center Publ., 95(2011), 339-351.

[4] Zygmund A., Trigonometric series, Cambridge, 2002.

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Mathematical Citation Quotient (MCQ) 2017: 0.08

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researchers in the fields of pure mathematics

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