{"title":"Convergence properties of new $$\\alpha $$ -Bernstein–Kantorovich type operators","authors":"Ajay Kumar, Abhishek Senapati, Tanmoy Som","doi":"10.1007/s13226-024-00577-5","DOIUrl":null,"url":null,"abstract":"<p>In the present paper, we introduce a new sequence of <span>\\(\\alpha -\\)</span>Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness for Lipschitz-type space and functions with derivatives of bounded variations.</p>","PeriodicalId":501427,"journal":{"name":"Indian Journal of Pure and Applied Mathematics","volume":"52 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Indian Journal of Pure and Applied Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13226-024-00577-5","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In the present paper, we introduce a new sequence of \(\alpha -\)Bernstein-Kantorovich type operators, which fix constant and preserve Korovkin’s other test functions in a limiting sense. We extend the natural Korovkin and Voronovskaja type results into a sequence of probability measure spaces. Then, we establish the convergence properties of these operators using the Ditzian-Totik modulus of smoothness for Lipschitz-type space and functions with derivatives of bounded variations.
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