文章基本信息
- 标题：A new inequality for a polynomial
- 本地全文：下载
- 作者：K. K. Dewan ; Harish Singh ; R. S. Yadav 等
- 期刊名称：International Journal of Mathematics and Mathematical Sciences
- 印刷版ISSN：0161-1712
- 电子版ISSN：1687-0425
- 出版年度：2001
- 卷号：28
- 期号：11
- 页码：679-684
- DOI：10.1155/S0161171201006032
- 出版社：Hindawi Publishing Corporation
- 摘要：
Let p ( z ) = a 0 + ∑ j = t n a j z j be a polynomial of degree n , having no zeros in | z | < k , k ≥ 1 then it has been shown that for R > 1 and | z | = 1 , | p ( R z ) − p ( z ) | ≤ ( R n − 1 ) ( 1 + A t B t K t + 1 ) / ( 1 + k t + 1 + A t B t ( k t + 1 + k 2 t ) ) max | z | = 1 | p ( z ) | − { 1 − ( 1 + A t B t k t + 1 ) / ( 1 + k t + 1 + A t B t ( k t + 1 + k 2 t ) ) } ( ( R n − 1 ) m / k n ) , where m = min | z | = k | p ( z ) | , 1 ≤ t < n , A t = ( R t − 1 ) / ( R n − 1 ) , and B t = | a t / a 0 | . Our result generalizes and improves some well-known results.
