On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness
In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2017-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2017/9323181 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832560377195397120 |
|---|---|
| author | Nimete Sh. Berisha Faton M. Berisha Mikhail K. Potapov Marjan Dema |
| author_facet | Nimete Sh. Berisha Faton M. Berisha Mikhail K. Potapov Marjan Dema |
| author_sort | Nimete Sh. Berisha |
| collection | DOAJ |
| description | In this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities. |
| format | Article |
| id | doaj-art-4a2c6d8a276b407faf81b0a4ac953de7 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4a2c6d8a276b407faf81b0a4ac953de72025-02-03T01:27:40ZengWileyAbstract and Applied Analysis1085-33751687-04092017-01-01201710.1155/2017/93231819323181On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of SmoothnessNimete Sh. Berisha0Faton M. Berisha1Mikhail K. Potapov2Marjan Dema3Faculty of Economics, University of Prishtina, Nëna Terezë 5, Prishtina, KosovoFaculty of Mathematics and Sciences, University of Prishtina, Prishtina, KosovoDepartment of Mechanics and Mathematics, Moscow State University, Moscow 117234, RussiaFaculty of Electrical and Computer Engineering, University of Prishtina, Prishtina, KosovoIn this paper, we give a characterization of Nikol’skiĭ-Besov type classes of functions, given by integral representations of moduli of smoothness, in terms of series over the moduli of smoothness. Also, necessary and sufficient conditions in terms of monotone or lacunary Fourier coefficients for a function to belong to such a class are given. In order to prove our results, we make use of certain recent reverse Copson-type and Leindler-type inequalities.http://dx.doi.org/10.1155/2017/9323181 |
| spellingShingle | Nimete Sh. Berisha Faton M. Berisha Mikhail K. Potapov Marjan Dema On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness Abstract and Applied Analysis |
| title | On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness |
| title_full | On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness |
| title_fullStr | On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness |
| title_full_unstemmed | On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness |
| title_short | On Approximations by Trigonometric Polynomials of Classes of Functions Defined by Moduli of Smoothness |
| title_sort | on approximations by trigonometric polynomials of classes of functions defined by moduli of smoothness |
| url | http://dx.doi.org/10.1155/2017/9323181 |
| work_keys_str_mv | AT nimeteshberisha onapproximationsbytrigonometricpolynomialsofclassesoffunctionsdefinedbymoduliofsmoothness AT fatonmberisha onapproximationsbytrigonometricpolynomialsofclassesoffunctionsdefinedbymoduliofsmoothness AT mikhailkpotapov onapproximationsbytrigonometricpolynomialsofclassesoffunctionsdefinedbymoduliofsmoothness AT marjandema onapproximationsbytrigonometricpolynomialsofclassesoffunctionsdefinedbymoduliofsmoothness |