{"title":"基于\\(q\\) -整数的Kantorovich型Lupaș-Stancu算子的近似定理","authors":"S. K. Serenbay, Özge Dalmanoglu","doi":"10.33993/jnaat461-1108","DOIUrl":null,"url":null,"abstract":"In this paper, we introduce a Kantorovich generalization of q-Stancu-Lupa¸s operators and investigate their approximation properties. The rate of convergence of these operators are obtained by means of modulus of continuity, functions of Lipschitz class and Peetre's K-functional. We also investigate the convergence of the operators in the statistical sense and give a numerical example in order to estimate the error in the approximation.","PeriodicalId":287022,"journal":{"name":"Journal of Numerical Analysis and Approximation Theory","volume":"65 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2017-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximation theorems for Kantorovich type Lupaș-Stancu operators based on \\\\(q\\\\)-integers\",\"authors\":\"S. K. Serenbay, Özge Dalmanoglu\",\"doi\":\"10.33993/jnaat461-1108\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we introduce a Kantorovich generalization of q-Stancu-Lupa¸s operators and investigate their approximation properties. The rate of convergence of these operators are obtained by means of modulus of continuity, functions of Lipschitz class and Peetre's K-functional. We also investigate the convergence of the operators in the statistical sense and give a numerical example in order to estimate the error in the approximation.\",\"PeriodicalId\":287022,\"journal\":{\"name\":\"Journal of Numerical Analysis and Approximation Theory\",\"volume\":\"65 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2017-09-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Numerical Analysis and Approximation Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.33993/jnaat461-1108\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Numerical Analysis and Approximation Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.33993/jnaat461-1108","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Approximation theorems for Kantorovich type Lupaș-Stancu operators based on \(q\)-integers
In this paper, we introduce a Kantorovich generalization of q-Stancu-Lupa¸s operators and investigate their approximation properties. The rate of convergence of these operators are obtained by means of modulus of continuity, functions of Lipschitz class and Peetre's K-functional. We also investigate the convergence of the operators in the statistical sense and give a numerical example in order to estimate the error in the approximation.
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