International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2001 / Article

Open Access

Volume 28 |Article ID 916325 | https://doi.org/10.1155/S016117120100607X

K. K. Dewan, Abdullah Mir, R. S. Yadav, "Integral mean estimates for polynomials whose zeros are within a circle", International Journal of Mathematics and Mathematical Sciences, vol. 28, Article ID 916325, 5 pages, 2001. https://doi.org/10.1155/S016117120100607X

Integral mean estimates for polynomials whose zeros are within a circle

Received03 Nov 2000

Abstract

Let p(z) be a polynomial of degree n having all its zeros in |z|k;k1, then for each r>0, p>1, q>1 with p1+q1=1, Aziz and Ahemad (1996) recently proved that n{02π|p(eiθ)|rdθ}1/r{02π|1+keiθ|prdθ}1/pr{02π|p(eiθ)|qrdθ}1/qr. In this paper, we extend the above inequality to the class of polynomials p(z)=anzn+v=μnanvznv;1μn having all its zeros in |z|k;k1 and obtain a generalization as well as a refinement of the above result.

Copyright © 2001 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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