# Some inequalities for polynomials satisfying p(z)≡z^{n}p(1/z)

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## Abstract

Let\(p\left( z \right) = \sum\limits_{\upsilon = 0}^n {a_\upsilon z^\upsilon } \) be a polynomial degreen and let\(\left\| p \right\| = \mathop {\max }\limits_{\left| x \right| = 1} \left| {p\left( z \right)} \right|\). Then according to Bernstein’s inequality ‖p’‖≤n‖p‖. It is a well known open problem to obtain inequality analogous to Bernstein’s inequality for the class II_{n} of polynomials satisfying p(z)≡z^{n}p(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of II_{n}. Our results include several of the known results as special cases.

## Keywords

Open Problem Complex Plane Simple Consequence Partial Result Polynomial Degree
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