Best trigonometric approximation and modulus of smoothness of functions in weighted grand Lebesgue spaces

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dc.contributor.author Jafarov, Sadulla Z.
dc.date.accessioned 2019-08-19T08:45:39Z
dc.date.available 2019-08-19T08:45:39Z
dc.date.issued 2019-06-28
dc.identifier.citation Jafarov, S.Z. Best trigonometric approximation and modulus of smoothness of functions in weighted grand Lebesgue spaces / S.Z. Jafarov // Қарағанды универисетінің хабаршысы. Математика сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series. – 2019. - № 2. – P. 26-32. ru_RU
dc.identifier.issn 2518-7929
dc.identifier.issn 2663-5011
dc.identifier.uri http://rep.ksu.kz//handle/data/7267
dc.description.abstract In this work, first of all, Lωp),Θ (T) weighted grand Lebesgue spaces and Muckenhoupt weights is defined. The information about properties of these spaces is given. Let Tn be the trigonometric polynomial of best approximation. The approximation of the functions in grand Lebesgue spaces have been investigated by many authors. In this work the relation between fractional derivatives of a Tn trigonımetric polynomial and the best approximation of the function is investigated in weighted grand Lebesgue spaces. In that regard, the neccessary and sufficient condition is expressed in Theorem 1. In addition, in this work in weighted grand Lebesgue spaces a specific operator is defined. Later on, with the help of this operator the fractional modules of smoothness of order r of function f is defined. Also, in this work, using the properties of modulus of smoothness of function, the relationship between the fractional modulus of smoothness of the function and n-th partial and de la Vall´ee-Poussin sums of its Fourier series in subspace of weighted grand Lebesgue spaces are studied. These results are expressed in Theorem 2. ru_RU
dc.language.iso en ru_RU
dc.publisher Ye.A.Buketov Karaganda State University Publishing house ru_RU
dc.relation.ispartofseries Қарағанды универисетінің хабаршысы. Математика Сериясы.=Вестник Карагандинского университета. Серия Математика.=Bulletin of the Karaganda University. Mathematics Series.;№ 2(94)/2019
dc.subject heneralized grand Lebesgue spaces ru_RU
dc.subject fractional derivative ru_RU
dc.subject fractional moduli of smoothness ru_RU
dc.subject n-th partial sums ru_RU
dc.subject de la Vall´ee-Poussin sums ru_RU
dc.subject best approximation by trigonometric polynomials ru_RU
dc.title Best trigonometric approximation and modulus of smoothness of functions in weighted grand Lebesgue spaces ru_RU
dc.title.alternative Ең жақын тригонометриялық жуықтау және Лебентің салмақтық гранд-кеңістіктеріндегі функцияның тегістігінің модулі ru_RU
dc.title.alternative Наилучшее тригонометрическое приближение и модуль гладкости функций в весовых гранд-пространствах Лебега ru_RU
dc.type Article ru_RU


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