{"title":"A generalization of modified \\(\\alpha \\)-Bernstein operators and its related estimations and errors","authors":"Jaspreet Kaur, Meenu Goyal, Khursheed J. Ansari","doi":"10.1007/s40065-024-00482-z","DOIUrl":null,"url":null,"abstract":"<div><p>In the present article, we introduce a novel generalization of modified Bernstein operators which is again a positive linear operator. We show the necessary and sufficient condition for the convergence of these operators. We also study some other approximation properties of these operators using standard tools of approximation theory.</p></div>","PeriodicalId":54135,"journal":{"name":"Arabian Journal of Mathematics","volume":"13 3","pages":"521 - 531"},"PeriodicalIF":0.9000,"publicationDate":"2024-11-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s40065-024-00482-z.pdf","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Arabian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s40065-024-00482-z","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In the present article, we introduce a novel generalization of modified Bernstein operators which is again a positive linear operator. We show the necessary and sufficient condition for the convergence of these operators. We also study some other approximation properties of these operators using standard tools of approximation theory.
期刊介绍：
The Arabian Journal of Mathematics is a quarterly, peer-reviewed open access journal published under the SpringerOpen brand, covering all mainstream branches of pure and applied mathematics.
Owned by King Fahd University of Petroleum and Minerals, AJM publishes carefully refereed research papers in all main-stream branches of pure and applied mathematics. Survey papers may be submitted for publication by invitation only.To be published in AJM, a paper should be a significant contribution to the mathematics literature, well-written, and of interest to a wide audience. All manuscripts will undergo a strict refereeing process; acceptance for publication is based on two positive reviews from experts in the field.Submission of a manuscript acknowledges that the manuscript is original and is not, in whole or in part, published or submitted for publication elsewhere. A copyright agreement is required before the publication of the paper.Manuscripts must be written in English. It is the author''s responsibility to make sure her/his manuscript is written in clear, unambiguous and grammatically correct language.
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