{"title":"On a special class of modified integral operators preserving some exponential functions","authors":"G. Uysal","doi":"10.3934/mfc.2021044","DOIUrl":null,"url":null,"abstract":"<p style='text-indent:20px;'>In the present paper, we consider a general class of operators enriched with some properties in order to act on <inline-formula><tex-math id=\"M1\">\\begin{document}$ C^{\\ast }( \\mathbb{R} _{0}^{+}) $\\end{document}</tex-math></inline-formula>. We establish uniform convergence of the operators for every function in <inline-formula><tex-math id=\"M2\">\\begin{document}$ C^{\\ast }( \\mathbb{R} _{0}^{+}) $\\end{document}</tex-math></inline-formula> on <inline-formula><tex-math id=\"M3\">\\begin{document}$ \\mathbb{R} _{0}^{+} $\\end{document}</tex-math></inline-formula>. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.</p>","PeriodicalId":93334,"journal":{"name":"Mathematical foundations of computing","volume":null,"pages":null},"PeriodicalIF":1.3000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical foundations of computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/mfc.2021044","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, THEORY & METHODS","Score":null,"Total":0}
引用次数: 1
Abstract
In the present paper, we consider a general class of operators enriched with some properties in order to act on \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}. We establish uniform convergence of the operators for every function in \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document} on \begin{document}$ \mathbb{R} _{0}^{+} $\end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.
In the present paper, we consider a general class of operators enriched with some properties in order to act on \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document}. We establish uniform convergence of the operators for every function in \begin{document}$ C^{\ast }( \mathbb{R} _{0}^{+}) $\end{document} on \begin{document}$ \mathbb{R} _{0}^{+} $\end{document}. Then, a quantitative result is proved. A quantitative Voronovskaya-type estimate is obtained. Finally, some applications are provided concerning particular kernel functions.
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