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Some inequalities for polynomials satisfying p(z)≡znp(1/z)

  • B. Datt
  • N. K. Govil
Article
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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 IIn of polynomials satisfying p(z)≡znp(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of IIn. Our results include several of the known results as special cases.

Keywords

Open Problem Complex Plane Simple Consequence Partial Result Polynomial Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer 1996

Authors and Affiliations

  • B. Datt
    • 1
  • N. K. Govil
    • 2
  1. 1.Department of Mathematics and StatisticsHaryana Agricultural UniversityHissarIndia
  2. 2.Department of MathematicsAuburn UniversityUSA

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