Share This Article:

On the Derivative of a Polynomial

Full-Text HTML XML Download Download as PDF (Size:142KB) PP. 746-749
DOI: 10.4236/am.2012.37110    4,924 Downloads   7,576 Views   Citations

ABSTRACT

Certain refinements and generalizations of some well known inequalities concerning the polynomials and their derivatives are obtained.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

N. Rather and M. Shah, "On the Derivative of a Polynomial," Applied Mathematics, Vol. 3 No. 7, 2012, pp. 746-749. doi: 10.4236/am.2012.37110.

References

[1] A. C. Schaffer, “Inequalities of A. Markoff and S. Bernstein for Polynomials and Related Functions,” Bulletin of the American Mathematical Society, Vol. 47, 1941, pp. 565-579. doi:10.1090/S0002-9904-1941-07510-5
[2] M. Riesz, “Uber Einen Satz des Herrn Serge Bernstein,” Acta Mathematica, Vol. 40, 1916, pp. 337-347. doi:10.1007/BF02418550
[3] G. Pólya and G. Szeg?, “Aufgaben und lehrs?tze aus der Analysis,” Springer-Verlag, Berlin, 1925.
[4] C. Frappier, Q. I. Rahman and St. Ruscheweyh, “New Inequalities for Polynomials,” Transactions of the American Mathematical Society, Vol. 288, 1985, pp. 69-99. doi:10.1090/S0002-9947-1985-0773048-1
[5] A. Aziz, “A Refinement of an Inequality of S.Bernstein,” Journal of Mathematical Analysis and Applications, Vol. 142, No. 1, 1989, pp. 226-235. doi:10.1016/0022-247X(89)90370-3
[6] P. D. Lax, “Proof of a Conjecture of P.Erd?s on the Derivative of a Polynomial,” Bulletin of the American Mathematical Society, Vol. 50, 1944, pp. 509-513. doi:10.1090/S0002-9904-1944-08177-9
[7] A. Aziz and Q. G. Mohammad, “Simple Proof of a Theorem of Erdos and Lax,” Proceedings of the American Mathematical Society, Vol. 80, 1980, pp. 119-122.
[8] A. Aziz and N. A. Rather, “New Lq Inequalities for Polynomials,” Mathematical Inequalities and Applications, Vol. 2, 1998, pp. 177-191. doi:10.7153/mia-01-16
[9] N. K. Govil and Q. I. Rahman, “Functions of Exponential Type Not Vanishing in a Half Plane and Related Polynomials,” Transactions of the American Mathematical Society, Vol. 137, 1969, pp. 501-517. doi:10.1090/S0002-9947-1969-0236385-6

  
comments powered by Disqus

Copyright © 2018 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.