Best approximations of periodic functions in generalized lebesgue spaces

Chaichenko, Stanislav

doi:10.1007/s11253-013-0725-6

Cited by 10 publications

(3 citation statements)

References 12 publications

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“…In recent decades, the topics related to the direct and inverse approximation theorems have been actively investigated in the Orlicz spaces and in the Lebesgue spaces with a variable exponent. In particular, for the Lebesgue functional spaces with variable exponent, similar results are contained in the papers of Guven and Israfilov [13], Akgün [2], Akgün and Kokilashvili [3,4], Chaichenko [8], Jafarov [14,15] and others. The latest results related to the Lebesgue spaces with variable exponent, and their applications are described in the monograph [10].…”

Section: Introductionsupporting

confidence: 52%

Direct and inverse approximation theorems in the weighted Orlicz-type spaceswith a variable exponent

Аbdullayev¹,

Chaichenko²,

kyzy³

et al. 2020

Turk J Math

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In weighted Orlicz type spaces S p, µ with a variable summation exponent, the direct and inverse approximation theorems are proved in terms of best approximations of functions and moduli of smoothness of fractional order. It is shown that the constant obtained in the inverse approximation theorem is in a certain sense the best. Some applications of the results are also proposed. In particular, the constructive characteristics of functional classes defined by such moduli of smoothness are given. Equivalence between moduli of smoothness and certain Peetre K-functionals is shown in the spaces S p, µ .

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Section: Introductionsupporting

confidence: 52%

Direct and inverse approximation theorems in the weighted Orlicz-type spaceswith a variable exponent

Аbdullayev¹,

Chaichenko²,

kyzy³

et al. 2020

Turk J Math

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“…In the space L q(•) ϑ (T) , similar theorems were obtained in the papers [3,7,10,18,23,25]. Variable exponent weighted Lebesgue spaces have important applications in the theory of elasticity, fluid dynamics, and differential equations [15,24].…”

Section: Introduction and Main Resultsmentioning

confidence: 63%

Jackson and Stechkin type inequalities of trigonometric approximation inAp;q()w;#

Avşar¹,

Koç²

2018

Turk J Math

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“…Also there are some estimates of best approximation and modulus of smoothness in Lebesgue spaces of periodic functions with transformed Fourier series in [13]. Approximation properties of functions having (ψ, β)-derivatives in variable exponent Lebesgue spaces which is a generalization of Lebesgue spaces was investigated in the papers [1,2,7].…”

Section: Introductionmentioning

confidence: 99%