{"title":"On Baskakov operators preserving the exponential function","authors":"Övgü Gürel Yılmaz, Gupta Vijay, A. Aral","doi":"10.33993/jnaat462-1110","DOIUrl":null,"url":null,"abstract":"In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions \\(e_{0}\\) and \\(e^{2ax},\\ a>0\\) fixed. \nUsing the modulus of continuity, we show the uniform convergence of new operators to \\(f\\). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"359 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat462-1110","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 17
Abstract
In this paper, we are concerned about the King-type Baskakov operators defined by means of the preserving functions \(e_{0}\) and \(e^{2ax},\ a>0\) fixed.
Using the modulus of continuity, we show the uniform convergence of new operators to \(f\). Also, by analyzing the asymptotic behavior of King-type operators with a Voronovskaya-type theorem, we establish shape preserving properties using the generalized convexity.
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