Some Sharpening and Generalizations of a Result of T. J. Rivlin
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...
Saved in:
| Published in | 分析理论与应用：英文刊 Vol. 33; no. 3; pp. 219 - 228 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | Chinese |
| Published |
2017
|
| Online Access | Get full text |
| ISSN | 1672-4070 1573-8175 |
Cover
| Summary: | 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. |
|---|---|
| Bibliography: | 32-1631/O1 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. Inequalities, polynomials, zeros. |
| ISSN: | 1672-4070 1573-8175 |