SOME GENERALIZATIONS OF POLYNOMIAL INEQUALITIES

Abstract

In this paper, we investigate the dependence of { \int_{0}^{2\pi} | P(Re^{i \theta}) - \beta P(re^{i \theta}) |^q d \theta }^{\frac{1}{q}} on { \int_{0}^{2 \pi} | P(e^{i \theta}) |^q d \theta }^{\frac{1}{q} } for each real or complex number \beta with \beta <=1, R > r >= 1 and q > 0 and present compact generalizations of some well-known polynomial inequalities.