Improvement and generalization of polynomial inequality of T. J. Rivlin

Autor: Devi, Maisnam Triveni, Singh, Thangjam Birkramjit, Chanam, Barchand
Zdroj: São Paulo Journal of Mathematical Sciences; 20220101, Issue: Preprints p1-11, 11p
Abstrakt: Let p(z) be a polynomial of degree nhaving no zero in |z|<1, then for r≤1, the famous result proved by Rivlin (Am. Math. Mon., 67:251–253, 1960) is max|z|=r|p(z)|≥1+r2nmax|z|=1|p(z)|.The inequality is sharp. In this paper, by involving some coefficients of the polynomial, we prove an inequality which not only improves as well as generalizes this inequality but also has some interesting consequences.
Databáze: Supplemental Index
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