{"title":"Inequalities for the First and Second Derivatives of Algebraic Polynomials on an Ellipse","authors":"Tatiana M. Nikiforova","doi":"10.1556/314.2021.00020","DOIUrl":null,"url":null,"abstract":"We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.","PeriodicalId":383314,"journal":{"name":"Mathematica Pannonica","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematica Pannonica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1556/314.2021.00020","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
We prove a theorem on the preservation of inequalities between functions of a special form after differentiation on an ellipse. In particular, we obtain generalizations of the Duffin–Schaeffer inequality and the Vidensky inequality for the first and second derivatives of algebraic polynomials to an ellipse.
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