{"title":"从相应的S.N. Bernstein型三角多项式估计连续$2\\pi$周期函数的偏差","authors":"N.Ya. Yatsenko","doi":"10.15421/247712","DOIUrl":null,"url":null,"abstract":"We have established the estimation of deviation of continuous $2\\pi$-periodic function $f(x)$ from the trigonometric polynomial of S.N. Bernstein's type that corresponds to it, by the modulus of continuity of the function $f(x)$.","PeriodicalId":52827,"journal":{"name":"Researches in Mathematics","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-10-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Estimation of deviation of continuous $2\\\\pi$-periodic functions from corresponding trigonometric polynomials of S.N. Bernstein's type\",\"authors\":\"N.Ya. Yatsenko\",\"doi\":\"10.15421/247712\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We have established the estimation of deviation of continuous $2\\\\pi$-periodic function $f(x)$ from the trigonometric polynomial of S.N. Bernstein's type that corresponds to it, by the modulus of continuity of the function $f(x)$.\",\"PeriodicalId\":52827,\"journal\":{\"name\":\"Researches in Mathematics\",\"volume\":\"21 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-10-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Researches in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15421/247712\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Researches in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15421/247712","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
Estimation of deviation of continuous $2\pi$-periodic functions from corresponding trigonometric polynomials of S.N. Bernstein's type
We have established the estimation of deviation of continuous $2\pi$-periodic function $f(x)$ from the trigonometric polynomial of S.N. Bernstein's type that corresponds to it, by the modulus of continuity of the function $f(x)$.
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