Some Sharpening and Generalizations of a Result of T. J. Rivlin  

作　　者：N.K.Govil Eze R.Nwaeze 

机构地区：[1]Department of Mathematics and Statistics, Auburn University [2]Department of Mathematics, Tuskegee University

出　　处：《Analysis in Theory and Applications》2017年第3期219-228,共10页分析理论与应用（英文刊）

摘　　要：Let p（z） = a0＋a1z＋a2z^2＋a3z3＋…＋anz^n be a polynomial of degree n. Rivlin [12] proved that if p （z） ≠ 0 in the unit disk, then for 0 〈 r ≤ 1,max（｜r＋1｜/2）^n max｜p（z）｜.｜z｜=1In this paper, we prove a sharpening and generalization of this result and show by means of examples that for some polynomials our result can significantly improve the bound obtained by the Rivlin＇s Theorem.Let p（z） = a0＋a1z＋a2z^2＋a3z3＋…＋anz^n be a polynomial of degree n. Rivlin [12] proved that if p （z） ≠ 0 in the unit disk, then for 0 〈 r ≤ 1,max（｜r＋1｜/2）^n max｜p（z）｜.｜z｜=1In this paper, we prove a sharpening and generalization of this result and show by means of examples that for some polynomials our result can significantly improve the bound obtained by the Rivlin＇s Theorem.

关 键 词：INEQUALITIES POLYNOMIALS zeros. 

分 类 号：O174.14[理学—数学]