{"title":"On the Erdös–Lax-Type Inequalities for Polynomials","authors":"I. Nazir, I. A. Wani","doi":"10.3103/s1068362324700195","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.3103/s1068362324700195","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
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Abstract
Erdös–Lax inequality relates the sup norm of the derivative of a polynomial along the unit circle to that of the polynomial itself (on the unit circle). This paper aims to extend the classical Erdös–Lax inequality to the polar derivative of a polynomial by using the extreme coefficients of the given polynomial. The obtained results not only enrich the realm of Erdös–Lax-type inequalities but also offer a promising avenue for diverse applications where these inequalities play a pivotal role. To illustrate the practical significance of our results, we present a numerical example. It vividly demonstrates that our bounds are considerably sharper than the existing ones in the extensive literature on this captivating subject.
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