{"title":"高阶Bernstein-Kantorovich算子","authors":"Anjali, Vijay Gupta","doi":"10.1007/s40010-022-00804-w","DOIUrl":null,"url":null,"abstract":"<div><p>In the present paper, we consider the higher-order (<i>j</i>-th order, <span>\\(j\\in \\textbf{N}_{0}\\)</span>) Bernstein–Kantorovich operators, which are connected with the Bernstein polynomials. We estimate some direct results including the Voronovskaja-kind asymptotic formula, simultaneous approximation and error estimations. In the end, we present comparative study through graphical representation and numerically interpret the upper bound of the error value.</p></div>","PeriodicalId":744,"journal":{"name":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-01-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Higher-Order Bernstein–Kantorovich Operators\",\"authors\":\"Anjali, Vijay Gupta\",\"doi\":\"10.1007/s40010-022-00804-w\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present paper, we consider the higher-order (<i>j</i>-th order, <span>\\\\(j\\\\in \\\\textbf{N}_{0}\\\\)</span>) Bernstein–Kantorovich operators, which are connected with the Bernstein polynomials. We estimate some direct results including the Voronovskaja-kind asymptotic formula, simultaneous approximation and error estimations. In the end, we present comparative study through graphical representation and numerically interpret the upper bound of the error value.</p></div>\",\"PeriodicalId\":744,\"journal\":{\"name\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-01-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences\",\"FirstCategoryId\":\"103\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s40010-022-00804-w\",\"RegionNum\":4,\"RegionCategory\":\"综合性期刊\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MULTIDISCIPLINARY SCIENCES\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the National Academy of Sciences, India Section A: Physical Sciences","FirstCategoryId":"103","ListUrlMain":"https://link.springer.com/article/10.1007/s40010-022-00804-w","RegionNum":4,"RegionCategory":"综合性期刊","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MULTIDISCIPLINARY SCIENCES","Score":null,"Total":0}
In the present paper, we consider the higher-order (j-th order, \(j\in \textbf{N}_{0}\)) Bernstein–Kantorovich operators, which are connected with the Bernstein polynomials. We estimate some direct results including the Voronovskaja-kind asymptotic formula, simultaneous approximation and error estimations. In the end, we present comparative study through graphical representation and numerically interpret the upper bound of the error value.
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