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