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Abstract

In this paper we consider a polynomial  having no zeros in the disk . We investigate the dependence of  on  and obtain a refinement of a famous result due to Rivilin ([5], [7]). Our results not only generalize some polynomial inequalities but also refine a result by Aziz [1].

 

 

Keywords

Growth of polynomials Maximum modulus Inequalities

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References

  1. Aziz, A. Growth of polynomials whose zeros are within or outside a circle. Bulletin of the Australian Mathematical Society, 1987, 35, 247-256.
  2. Aziz, A. and Mohammad, Q.G. Simple proof of a Theorem of Erdos and Lax. Proceedings of the American Mathematical Society, 1980, 80, 119-122.
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  4. Dewan, K.K. and Hans, S. Growth of polynomials whose zeros are outside a circle, Annales Universitates Mariae Curie-Sklodowska Lublin-Polonia, LXII, 2008, 61-65.
  5. Rahman, Q.I. and Schmeisser, G. Analytic Theory of Polynomials, Oxford University Press, New York, 2002.
  6. Riesz, M. Über einen satz des Herrn Serge Bernstein, Acta Mathematica, 2007, 40(3), 3069- 3075.
  7. Rivilin, T.J. On the maximum modulus of polynomials, American Mathematical Monthly, 1960, 67, 251-253.