Share This Article:

Inequalities for the Polar Derivative of a Polynomial

Abstract Full-Text HTML Download Download as PDF (Size:98KB) PP. 23-27
DOI: 10.4236/apm.2011.12006    4,959 Downloads   11,709 Views   Citations

ABSTRACT

If is a polynomial of degree , having all its zeros in |z|≤K, K≥1 , then it was proved by Aziz and Rather [2] that for every real or complex number with |a| ≥K, . In this paper, we sharpen above result for the polynomials p(z) of degree n>3

Cite this paper

G. Singh, W. Shah and Y. Paul, "Inequalities for the Polar Derivative of a Polynomial," Advances in Pure Mathematics, Vol. 1 No. 2, 2011, pp. 23-27. doi: 10.4236/apm.2011.12006.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] A. Aziz and Q. M. Dawood, “Inequalities for a Polynomial and its Derivative,” Journal of Approximation Theory, Vol. 54, No. 3, 1998, pp. 306-313.
[2] A. Aziz and N. A. Rather, “A Re-finement of a Theorem of Paul Turán Concerning Polynomi-als,” Journal of Mathematical Inequality Application, Vol. 1, No. 2, 1998, pp. 231-238.
[3] N. G. de Bruijn, “Inequalities Concerning Polynomials in the Complex Domain,” Nederl. Akad. Wetench. Proc. Ser. A, Vol. 50, 1947, pp. 1265-1272; Indagationes Mathematicae, Vol. 9, 1947, pp. 591-598.
[4] K. K. Dewan, N. Singh and A. Mir, “Growth of Polyno-mials not Vanishing inside a Circle,” International Journal of Mathematical Analysis, Vol. 1, No. 11, 2007, pp. 529-538.
[5] N. K. Govil, “On the Derivative of a Polynomial,” Pro-ceedings of the American Mathematical Society, Vol. 41, 1973, pp. 543-546. doi:10.1090/S0002-9939-1973-0325932-8
[6] P. D. Lax, “Proof of a Conjecture of P. Erd?s on the Derivative of a Polynomial,” American Mathematical Society, Vol. 50, No. 8, 1994, pp. 509-513.
[7] M. A. Malik, “On the Derivative of a Polynomial,” Journal of the London Mathematical Society, Vol. 2, No. 1, 1969, pp. 57-60. doi:10.1112/jlms/s2-1.1.57
[8] Polya and G. Szeg?, “Aus-gaben und Lehratze ous der Analysis,” Springer-Verlag, Berlin, 1995.
[9] W. M. Shah, “A Generalization of a Theorem of Paul Turán,” Journal Ramanujan Mathematical Society, Vol. 11, 1996, pp. 67-72.
[10] P. Turán, “über die Ableitung von Polynomen,” Compositio Mathematica, Vol. 7, 1939, pp. 89-95.

  
comments powered by Disqus

Copyright © 2020 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.