On the degree of approximation of Fourier series based on a certain class of product deferred summability means
Abstract In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions. We then estimate the degree of approximation of Fourier series of an arbitrary periodic function in the genera...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2023-02-01
|
| Series: | Journal of Inequalities and Applications |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13660-023-02927-z |
| _version_ | 1811171513526648832 |
|---|---|
| author | Bidu Bhusan Jena Susanta Kumar Paikray M. Mursaleen |
| author_facet | Bidu Bhusan Jena Susanta Kumar Paikray M. Mursaleen |
| author_sort | Bidu Bhusan Jena |
| collection | DOAJ |
| description | Abstract In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions. We then estimate the degree of approximation of Fourier series of an arbitrary periodic function in the generalized Zygmund class based upon our proposed product deferred summability means. Moreover, we discuss some important concluding remarks in connection with our findings. Finally, we suggest a direction for future studies on this subject, which are based upon the basic notion of statistical product deferred summability means of Fourier series of arbitrary periodic functions in the generalized Zygmund class. |
| first_indexed | 2024-04-10T17:15:16Z |
| format | Article |
| id | doaj.art-83df98981ae44be6966189cd53fcedcd |
| institution | Directory Open Access Journal |
| issn | 1029-242X |
| language | English |
| last_indexed | 2024-04-10T17:15:16Z |
| publishDate | 2023-02-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-83df98981ae44be6966189cd53fcedcd2023-02-05T12:26:53ZengSpringerOpenJournal of Inequalities and Applications1029-242X2023-02-012023111310.1186/s13660-023-02927-zOn the degree of approximation of Fourier series based on a certain class of product deferred summability meansBidu Bhusan Jena0Susanta Kumar Paikray1M. Mursaleen2Department of Mathematics, Veer Surendra Sai University of TechnologyDepartment of Mathematics, Veer Surendra Sai University of TechnologyDepartment of Medical Research, China Medical University Hospital, China Medical University (Taiwan)Abstract In this article, we first introduce and study the basic concepts of deferred Euler and deferred Nörlund product summability means of Fourier series of arbitrary periodic functions. We then estimate the degree of approximation of Fourier series of an arbitrary periodic function in the generalized Zygmund class based upon our proposed product deferred summability means. Moreover, we discuss some important concluding remarks in connection with our findings. Finally, we suggest a direction for future studies on this subject, which are based upon the basic notion of statistical product deferred summability means of Fourier series of arbitrary periodic functions in the generalized Zygmund class.https://doi.org/10.1186/s13660-023-02927-zDegree of approximationZygmund modulus of continuityFourier series of arbitrary periodic functionsDeferred Euler summability meanDeferred Nörlund summability meanProduct deferred summability mean |
| spellingShingle | Bidu Bhusan Jena Susanta Kumar Paikray M. Mursaleen On the degree of approximation of Fourier series based on a certain class of product deferred summability means Journal of Inequalities and Applications Degree of approximation Zygmund modulus of continuity Fourier series of arbitrary periodic functions Deferred Euler summability mean Deferred Nörlund summability mean Product deferred summability mean |
| title | On the degree of approximation of Fourier series based on a certain class of product deferred summability means |
| title_full | On the degree of approximation of Fourier series based on a certain class of product deferred summability means |
| title_fullStr | On the degree of approximation of Fourier series based on a certain class of product deferred summability means |
| title_full_unstemmed | On the degree of approximation of Fourier series based on a certain class of product deferred summability means |
| title_short | On the degree of approximation of Fourier series based on a certain class of product deferred summability means |
| title_sort | on the degree of approximation of fourier series based on a certain class of product deferred summability means |
| topic | Degree of approximation Zygmund modulus of continuity Fourier series of arbitrary periodic functions Deferred Euler summability mean Deferred Nörlund summability mean Product deferred summability mean |
| url | https://doi.org/10.1186/s13660-023-02927-z |
| work_keys_str_mv | AT bidubhusanjena onthedegreeofapproximationoffourierseriesbasedonacertainclassofproductdeferredsummabilitymeans AT susantakumarpaikray onthedegreeofapproximationoffourierseriesbasedonacertainclassofproductdeferredsummabilitymeans AT mmursaleen onthedegreeofapproximationoffourierseriesbasedonacertainclassofproductdeferredsummabilitymeans |