{"title":"The family of $ \\lambda $-Bernstein-Durrmeyer operators based on certain parameters","authors":"Ram Pratap","doi":"10.3934/mfc.2022038","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>The primary goal of this paper is to present the generalization of <inline-formula><tex-math id=\"M2\">\\begin{document}$ \\lambda $\\end{document}</tex-math></inline-formula>-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [<xref ref-type=\"bibr\" rid=\"b24\">24</xref>]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical foundations of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mfc.2022038","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 0
Abstract
The primary goal of this paper is to present the generalization of \begin{document}$ \lambda $\end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.
The primary goal of this paper is to present the generalization of \begin{document}$ \lambda $\end{document}-Bernstein operators with the assistance of a sequence of operators proposed by Mache and Zhou [24]. For these operators, I establish some approximation results using second-order modulus of continuity, Lipschitz space, Ditzian-Totik modulus of smoothness, and Voronovskaya type asymptotic results. I also indicate some graphical comparisons of my operators among existing operators for better presentation and justification using Matlab.
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