马立克的一个不等式注释

IF 1 4区数学 Q1 MATHEMATICS

Applicable Analysis and Discrete Mathematics Pub Date : 2022-01-01 DOI:10.2298/aadm210529030m

A. Mir, Abrar Ahmad, A. Malik

{"title":"马立克的一个不等式注释","authors":"A. Mir, Abrar Ahmad, A. Malik","doi":"10.2298/aadm210529030m","DOIUrl":null,"url":null,"abstract":"Let P(z):= ?nv=0 avzv be a univariate complex coefficient polynomial of degree n. It was shown by Malik [J London Math Soc, 1 (1969), 57-60] that if P(z) has all its zeros in |z| ? k, k ? 1, then max|z|=1 |P?(z)| ? n 1 + k max |z|=1 |P(z)|. In this paper, we prove an inequality for the polar derivative of a polynomial which besides give extensions and refinements of the above inequality also produce various inequalities that are sharper than the previous ones known in very rich literature on this subject.","PeriodicalId":51232,"journal":{"name":"Applicable Analysis and Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Note on an inequality of M.A. Malik\",\"authors\":\"A. Mir, Abrar Ahmad, A. Malik\",\"doi\":\"10.2298/aadm210529030m\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let P(z):= ?nv=0 avzv be a univariate complex coefficient polynomial of degree n. It was shown by Malik [J London Math Soc, 1 (1969), 57-60] that if P(z) has all its zeros in |z| ? k, k ? 1, then max|z|=1 |P?(z)| ? n 1 + k max |z|=1 |P(z)|. In this paper, we prove an inequality for the polar derivative of a polynomial which besides give extensions and refinements of the above inequality also produce various inequalities that are sharper than the previous ones known in very rich literature on this subject.\",\"PeriodicalId\":51232,\"journal\":{\"name\":\"Applicable Analysis and Discrete Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applicable Analysis and Discrete Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.2298/aadm210529030m\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applicable Analysis and Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.2298/aadm210529030m","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

设P(z):= ?nv=0 avzv是n次的单变量复系数多项式。Malik [J London Math Soc, 1(1969)， 57-60]证明了如果P(z)的所有零都在|z| ?K, K ?1，则max|z|=1 |P?(z)| ?n 1 + k max |z|=1 |P(z)|。在本文中，我们证明了一个多项式的极坐标导数的不等式，该不等式除了给出上述不等式的推广和改进外，还产生了各种不等式，这些不等式比以前在非常丰富的文献中已知的不等式更尖锐。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Note on an inequality of M.A. Malik

Let P(z):= ?nv=0 avzv be a univariate complex coefficient polynomial of degree n. It was shown by Malik [J London Math Soc, 1 (1969), 57-60] that if P(z) has all its zeros in |z| ? k, k ? 1, then max|z|=1 |P?(z)| ? n 1 + k max |z|=1 |P(z)|. In this paper, we prove an inequality for the polar derivative of a polynomial which besides give extensions and refinements of the above inequality also produce various inequalities that are sharper than the previous ones known in very rich literature on this subject.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Applicable Analysis and Discrete Mathematics MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

11.10%

发文量

审稿时长

>12 weeks

期刊介绍： Applicable Analysis and Discrete Mathematics is indexed, abstracted and cover-to cover reviewed in: Web of Science, Current Contents/Physical, Chemical & Earth Sciences (CC/PC&ES), Mathematical Reviews/MathSciNet, Zentralblatt für Mathematik, Referativny Zhurnal-VINITI. It is included Citation Index-Expanded (SCIE), ISI Alerting Service and in Digital Mathematical Registry of American Mathematical Society (http://www.ams.org/dmr/).