{"title":"锐化多项式的 Tur´an 型不等式","authors":"N. A. Rather, A. Bhat, M. Shafi","doi":"10.26907/0021-3446-2024-4-39-46","DOIUrl":null,"url":null,"abstract":"For the polynomial P(z) = n \\sum j=0 cjzj of degree n having all its zeros in | z| \\leq k, k \\geq 1, V. Jain in “On the derivative of a polynomial”, Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that max | z| =1 | P \\prime (z)| \\geq n \\biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) \\biggr) max | z| =1 | P(z)| . In this paper we strengthen the above inequality and other related results for the polynomials of degree n \\geq 2.","PeriodicalId":507800,"journal":{"name":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","volume":"27 2","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-04-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Sharpening of Tur´an-type inequality for polynomials\",\"authors\":\"N. A. Rather, A. Bhat, M. Shafi\",\"doi\":\"10.26907/0021-3446-2024-4-39-46\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For the polynomial P(z) = n \\\\sum j=0 cjzj of degree n having all its zeros in | z| \\\\leq k, k \\\\geq 1, V. Jain in “On the derivative of a polynomial”, Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that max | z| =1 | P \\\\prime (z)| \\\\geq n \\\\biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) \\\\biggr) max | z| =1 | P(z)| . In this paper we strengthen the above inequality and other related results for the polynomials of degree n \\\\geq 2.\",\"PeriodicalId\":507800,\"journal\":{\"name\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"volume\":\"27 2\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-04-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.26907/0021-3446-2024-4-39-46\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.26907/0021-3446-2024-4-39-46","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
对于多项式 P(z) = n \sum j=0 cjzj of degree n，其所有零点都在|z| \leq k, k \geq 1，V. Jain 在 "论多项式的导数"，Bull.Math.Soc.Roumanie Tome 59, 339-347 (2016) 证明了 max | z| =1 | P \prime (z)| \geq n \biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) \biggr) max | z| =1 | P(z)| 。本文将对 n \geq 2 度的多项式加强上述不等式及其它相关结果。
Sharpening of Tur´an-type inequality for polynomials
For the polynomial P(z) = n \sum j=0 cjzj of degree n having all its zeros in | z| \leq k, k \geq 1, V. Jain in “On the derivative of a polynomial”, Bull. Math. Soc. Sci. Math. Roumanie Tome 59, 339–347 (2016) proved that max | z| =1 | P \prime (z)| \geq n \biggl( | c0| + | cn| kn+1 | c0| (1 + kn+1) + | cn| (kn+1 + k2n) \biggr) max | z| =1 | P(z)| . In this paper we strengthen the above inequality and other related results for the polynomials of degree n \geq 2.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
