{"title":"Direct and converse theorems for King type operators","authors":"Z. Finta","doi":"10.3934/mfc.2022015","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>For a sequence of King type operators which preserve the functions <inline-formula><tex-math id=\"M1\">\\begin{document}$ e_0(x)=1 $\\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=\"M2\">\\begin{document}$ e_j(x)=x^j $\\end{document}</tex-math></inline-formula>, we establish a direct approximation theorem via the first order Ditzian-Totik modulus of smoothness, and a converse result of Berens-Lorentz type.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":"221 1","pages":"379-387"},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical foundations of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mfc.2022015","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1
Abstract
For a sequence of King type operators which preserve the functions \begin{document}$ e_0(x)=1 $\end{document} and \begin{document}$ e_j(x)=x^j $\end{document}, we establish a direct approximation theorem via the first order Ditzian-Totik modulus of smoothness, and a converse result of Berens-Lorentz type.
For a sequence of King type operators which preserve the functions \begin{document}$ e_0(x)=1 $\end{document} and \begin{document}$ e_j(x)=x^j $\end{document}, we establish a direct approximation theorem via the first order Ditzian-Totik modulus of smoothness, and a converse result of Berens-Lorentz type.
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