{"title":"On the maximum modulus of a complex polynomial","authors":"S. Malik, Ashish Kumar","doi":"10.31801/cfsuasmas.989344","DOIUrl":null,"url":null,"abstract":"In this paper we impose distinct restrictions on the moduli of the zeros of p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate the dependence of ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 on MαMα and Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p(z)p(z). This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p(1−wn)p(1−wn), $0<w\\leq$ given $p(1)=0$ is considered.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2022-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.989344","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 this paper we impose distinct restrictions on the moduli of the zeros of p(z)=n∑v=0avzvp(z)=∑v=0navzv and investigate the dependence of ∥p(Rz)−p(σz)∥‖p(Rz)−p(σz)‖, R>σ≥1R>σ≥1 on MαMα and Mα+πMα+π, where Mα=max1≤k≤n|p(ei(α+2kπ)/n)|Mα=max1≤k≤n|p(ei(α+2kπ)/n)| and on certain coefficients of p(z)p(z). This paper comprises several results, which in particular yields some classical polynomial inequalities as special cases. Moreover, the problem of estimating p(1−wn)p(1−wn), $0