Approximation of functions from $L^{p}(ω)_{β}$ by general linear operators of their Fourier series

Włodzimierz Łenski; Bogdan Szal

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On the pointwise strong approximation by (C,1)(E,1) means

Włodzimierz Łenski, Bogdan Roszak (2008)

Banach Center Publications

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We present an estimate of the (C,1)(E,1)-strong means with mixed powers of the Fourier series of a function $f \in L_{2 π}$ as a generalization of the result obtained by M. Yildrim and F. Karakus. Some corollaries on the norm approximation are also given.

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P. L. Sharma, R. K. Jain (1970)

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P. L. Sharma, V. Prakash, S. K. Varma (1985)

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The degree of approximation by Hausdorff means of a conjugate Fourier series

Sergiusz Kęska (2016)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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The purpose of this paper is to analyze the degree of approximation of a function $\bar{f}$ that is a conjugate of a function $f$ belonging to the Lipschitz class by Hausdorff means of a conjugate series of the Fourier series.

Approximation of functions from $L^{p} {(ω ̃)}_{β}$ by linear operators of conjugate Fourier series

WŁodzimierz Łenski, Bogdan Szal (2011)

Banach Center Publications

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We show the results corresponding to some theorems of S. Lal and H. K. Nigam [Int. J. Math. Math. Sci. 27 (2001), 555-563] on the norm and pointwise approximation of conjugate functions and to the results of the authors [Acta Comment. Univ. Tartu. Math. 13 (2009), 11-24] also on such approximations.

On embeddings of function classes defined by constructive characteristics

Boris V. Simonov, Sergey Yu. Tikhonov (2006)

Banach Center Publications

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In this paper we study embedding theorems for function classes which are subclasses of $L_{p}$ , 1 ≤ p ≤ ∞. To define these classes, we use the notion of best trigonometric approximation as well as that of a (λ,β)-derivative, which is the generalization of a fractional derivative. Estimates of best approximations of transformed Fourier series are obtained.

On the inclusion relation between strong $(J, p_{n})$ and strong $(\bar{N}, p_{n})$ summability methods

R. K. Jain, A. Ganguly (1978)

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Relations among K $S (λ)$ and certain other methods for evaluations of sequences and series

B. Martić (1964)

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On the $C^{α} | C^{β}$ convergence

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On generalized absolute Cesaro summability factors

A. Nihal Tuncer (2002)

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Using δ-quasi-monotone and any almost increasing sequences we prove a theorem on ${| C, α, β; δ |}_{k}$ summability factors of infinite series, which generalizes a theorem of Mazhar [7] on ${| C, 1 |}_{k}$ summability factors.

Functions in $L_{p}$ -space and their approximations

P. Chandra (1988)

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On the Nörlund means of Vilenkin-Fourier series

István Blahota, Lars-Erik Persson, Giorgi Tephnadze (2015)

Czechoslovak Mathematical Journal

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We prove and discuss some new $(H_{p}, L_{p})$ -type inequalities of weighted maximal operators of Vilenkin-Nörlund means with non-increasing coefficients ${q_{k} : k \geq 0}$ . These results are the best possible in a special sense. As applications, some well-known as well as new results are pointed out in the theory of strong convergence of such Vilenkin-Nörlund means. To fulfil our main aims we also prove some new estimates of independent interest for the kernels of these summability results. In the special cases of...

Lebesgue type points in strong (C,α) approximation of Fourier series

Włodzimierz Łenski, Bogdan Roszak (2011)

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We present an estimation of the $H_{k ₀, k_{r}}^{q, α} f$ and $H_{λ, u}^{ϕ, α} f$ means as approximation versions of the Totik type generalization (see [5], [6]) of the result of G. H. Hardy, J. E. Littlewood. Some corollaries on the norm approximation are also given.

Translativity of absolute weighted mean summability

Cihan Orhan (1998)

Czechoslovak Mathematical Journal

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In this paper, we give necessary and sufficient conditions on $(p_{n})$ for $| R, p_{n} |_{k}$ , $k \geq 1$ , to be translative. So we extend the known results of Al-Madi [1] and Cesco $[4]$ to the case $k > 1$ .

The polynomial approximation of continuous functions defined on $(- \infty, \infty)$

Leetsch C. Hsu (1959)

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Displaying similar documents to “Approximation of functions from L p ( ω ) β by general linear operators of their Fourier series”

Displaying similar documents to “Approximation of functions from $L^{p} {(ω)}_{β}$ by general linear operators of their Fourier series”