{"title":"Approximation of integrable functions by general linear matrix operators of their Fourier series","authors":"V. Mishra, W. Łenski, B. Szal","doi":"10.1515/dema-2022-0009","DOIUrl":null,"url":null,"abstract":"Abstract The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(\\cdot )-f\\left(\\cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the rth differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.","PeriodicalId":10995,"journal":{"name":"Demonstratio Mathematica","volume":null,"pages":null},"PeriodicalIF":2.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Demonstratio Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/dema-2022-0009","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract The pointwise estimates of the deviation T n , A f ( ⋅ ) − f ( ⋅ ) {T}_{n,A}f(\cdot )-f\left(\cdot ) in terms of pointwise moduli of continuity based on the points of differentiability of indefinite integral of f f , with application of the rth differences of the entries of A A , are proved. The similar results in case of the Lebesgue points are considered, too. Analogical results on norm approximation with remarks and corollaries are also given.
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Demonstratio Mathematica publishes original and significant research on topics related to functional analysis and approximation theory. Please note that submissions related to other areas of mathematical research will no longer be accepted by the journal. The potential topics include (but are not limited to): -Approximation theory and iteration methods- Fixed point theory and methods of computing fixed points- Functional, ordinary and partial differential equations- Nonsmooth analysis, variational analysis and convex analysis- Optimization theory, variational inequalities and complementarity problems- For more detailed list of the potential topics please refer to Instruction for Authors. The journal considers submissions of different types of articles. "Research Articles" are focused on fundamental theoretical aspects, as well as on significant applications in science, engineering etc. “Rapid Communications” are intended to present information of exceptional novelty and exciting results of significant interest to the readers. “Review articles” and “Commentaries”, which present the existing literature on the specific topic from new perspectives, are welcome as well.
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