{"title":"On Weighted Lp-Approximation by Weighted Bernstein-Durrmeyer Operators","authors":"Meili Wang","doi":"10.4208/ATA.2018.V34.N1.1","DOIUrl":null,"url":null,"abstract":"Abstract. In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted Lp−norm with Jacobi weight w(x) = xα(1−x). All the results involved have no restriction α,β< 1− p , which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.","PeriodicalId":29763,"journal":{"name":"Analysis in Theory and Applications","volume":"24 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis in Theory and Applications","FirstCategoryId":"95","ListUrlMain":"https://doi.org/10.4208/ATA.2018.V34.N1.1","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Abstract. In the present paper, we establish direct and converse theorems for weighted Bernstein-Durrmeyer operators under weighted Lp−norm with Jacobi weight w(x) = xα(1−x). All the results involved have no restriction α,β< 1− p , which indicates that the weighted Bernstein-Durrmeyer operators have some better approximation properties than the usual Bernstein-Durrmeyer operators.
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