V.K. Jain: Inequalities for polynomials with a prescribed zero, p.441-449

Abstract:

For a polynomial $p(z)$ of degree $n$, with $p(\beta)=0$, we have obtained a generalization of an integral inequality, (due to Callahan), involving mean value of $\vert p(z)\vert^2$ on unit circle, and by further assuming the zero of $p(z)$ at $\beta$, to be of order at least $k, (\geq 1)$, we have obtained generalizations of three other integral inequalities, (one, due to Donaldson $\&$ Rahman and two, due to Aziz), involving mean value of

$\vert p(z)/(z-\beta)\vert^2$ on unit circle. Certain other related results are also given.

Key Words: Inequalities, polynomial with a prescribed zero.

2000 Mathematics Subject Classification: Primary: 30C10,
Secondary: 30A10.

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