Some Extensions of a Theorem of Paul Turán Concerning Polynomials
Download PDF
Authors: N. A. RATHER, I. DAR AND A. IQBAL
DOI: 10.46793/KgJMat2206.969R
Abstract:
In this paper, certain new results concerning the maximum modulus of the polar derivative of a polynomial with restricted zeros are obtained. These estimates strengthen some well known inequalities for polynomial due to Turán, Dubinin and others.
Keywords:
Polynomials, polar derivative, inequalities in the complex domain.
References:
[1] A. Aziz, Inequalities for the derivative of a polynomial, Proc. Amer. Math. Soc. 89 (1983), 259–266.
[2] A. Aziz and Q. M. Dawood, Inequalities for a polynomial and its derivatives, J. Approx. Theory 54 (1998), 306–313.
[3] A. Aziz and N. A. Rather, Some Zygmund type Lq inequalities for polynomials, J. Math. Anal. Appl. 289 (2004), 14–29.
[4] A. Aziz and N. A. Rather, Inequalities for the polar derivative of a polynomial with restricted zeros, Math. Balkanica 17 (2003), 15–28.
[5] A. Aziz and N. A. Rather, A refinement of a theorem of Paul Turán concerning polynomials, Math. Inequal. Appl. 1 (1998), 231–238.
[6] V. N. Dubinin, Distortion theorems for polynomials on a circle, Sb. Math. 191(12) (2000), 1797–1807.
[7] C. Frappier, Q. I. Rahman and St. Ruscheweyh, New inequalities for polynomials, Trans. Amer. Math. Soc. 288 (1985), 69–99.
[8] N. K. Govil, On the derivative of a polynomial, Proc. Amer. Math. Soc. 41 (1973), 543–546.
[9] P. D. Lax, Proof of a conjecture of P. Erdös on the derivative of a polynomial, Bull. Amer. Math. Soc. 50 (1944), 509–513.
[10] M. Marden, Geometry of Polynomials, Amer. Math. Soc., Math. Surveys 3, Providence, 1966.
[11] G. V. Milovanović, D. S. Mitrinović and Th. M. Rassias, Topics in Polynomials: Extremal Properties, Inequalities, Zeros, World scientific Publishing Co., Singapore, 1994.
[12] G. P
lya and G. Szeg
, Problems and Theorems in Analysis,
II, Springer-Verlag, Berlin, New York, 1976.
[13] N. A. Rather and S. Gulzar, Generalization of an inequality involving maximum moduli of a polynomial and its polar derivative, Nonlinear Functional Analysis and Applications 19 (2014), 213–221.
[14] N. A. Rather and S. Gulzar, Refinements of some inequalities concerning the polar derivative of a polynomial, Funct. Approx. Comment. Math. 51 (2014), 269–283.
[15] S. Gulzar and N. A. Rather, Inequalities concerning the polar derivative of a polynomial, Bull. Malays. Math. Sci. Soc. 40 (2017), 1691–1700.
[16] P. Turán, Über die ableitung von polynomen, Compos. Math. 7 (1939), 89–95.
Login:
