AM  Vol.3 No.7 , July 2012
On the Derivative of a Polynomial
ABSTRACT
Certain refinements and generalizations of some well known inequalities concerning the polynomials and their derivatives are obtained.

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

 
 
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