Inequalities Concerning the Growth of Polynomials

Bashir A.Zargar, Ahmad W.Manzoor

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


Aziz, A. Growth of polynomials whose zeros are within or outside a circle. Bulletin of the Australian Mathematical Society, 1987, 35, 247-256.

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.

Dubinin, V.N. Applications of Schwarz Lemma to inequalities for entire functions with constraints on zeros, Journal of Mathematical Sciences, 2007, 143(3), 3069-3075.

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.

Rahman, Q.I. and Schmeisser, G. Analytic Theory of Polynomials, Oxford University Press, New York, 2002.

Riesz, M. Über einen satz des Herrn Serge Bernstein, Acta Mathematica, 2007, 40(3), 3069- 3075.

Rivilin, T.J. On the maximum modulus of polynomials, American Mathematical Monthly, 1960, 67, 251-253.




DOI: http://dx.doi.org/10.24200/squjs.vol23iss1pp68-72

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