Geodesic
Inequalities concerning $B$-operators
Problemy analiza, Tome 5 (2016) no. 1, pp. 55-72.

Voir la notice de l'article provenant de la source Math-Net.Ru

Let $\mathcal{P}_{n}$ be the class of polynomials of degree at most $n.$ Rahman introduced the class $\mathcal {B}_{n}$ of operators $B$ that map $\mathcal {P}_{n}$ into itself. In this paper we prove some results concerning such operators and thereby obtain generalizations of some well known polynomial inequalities.
Keywords: polynomials; $B$-operator; inequalities in the complex domain; zeros. 
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S. L. Wali; W. M. Shah; A. Liman. Inequalities concerning $B$-operators. Problemy analiza, Tome 5 (2016) no. 1, pp. 55-72. http://geodesic.mathdoc.fr/item/PA_2016_5_1_a4/

[1] Bernstein S., “Sur la limitation des dérivées des polynomes”, C. R. Acad. Sci. Paris, 190 (1930), 338–340

[2] Polya G., Szego G., Problems and Theorems in Analysis, New York, Springer Verlag

[3] Lax P. D., “Proof of a conjecture of P. Erdös on the derivative of a polynomial”, Bull. Amer. Math. Soc., 50 (1944), 509–513 | DOI | MR | Zbl

[4] Ankeny N. C., Rivlin T. J., “On a Theorem of S. Bernstein”, Pacific. J. Math., 5 (1955), 849–852 | DOI | MR | Zbl

[5] Frappier C., Rahman Q. I., Ruscheweyh St., “New inequalities for polynomials”, Trans. Amer. Math. Soc., 88 (1985), 69–99 | DOI | MR

[6] Bernstein S., Lecons Sur les propriétés extrémales et la meilleure approximation des function analytiques dúne variable réele, Gauthier-Villars, Paris, 1926

[7] Govil N. K., “On the derivative of a polynomial”, Proc. Amer. Math. Soc., 41 (1973), 543–546 | DOI | MR | Zbl

[8] Rahman Q. I., Schmeisser G., Analytic Theory of Polynomials, Oxford University Press, New York, 2002 | MR | Zbl

[9] Rahman Q. I., “Functions of exponential type”, Trans. Amer. Math. Soc., 135 (1969), 295–309 | DOI | MR | Zbl

[10] Marden M., Geometry of polynomials, Mathematical Surveys, 3, 2nd ed., Amer. Math. Soc., Providence, RI, 1966 | MR | Zbl

[11] Shah W. M., Liman A., “An operator preserving inequalities between polynomials”, J. Inequal. Pure Appl. Math., 9 (2008), 1–12 | MR | Zbl

[12] Govil N. K., Liman N. K., Shah W. M., “Some inequalities concerning derivative and maximum modulus of polynomials”, Aust. J. Math. Anal. Appl., 8 (2011), 1–8 | MR | Zbl

[13] Aziz A., Rather N. A., “Some compact generalizations of Zygmund type inequalities for polynomials”, Nonlinear Studies, 6 (1999), 241–255 | MR | Zbl

[14] Aziz A., Dawood Q. M., “Inequalities for a polynomial and its derivative”, J. Approx. Theory, 53 (1988), 155–162 | DOI | MR

[15] Aziz A., Zargar B. A., “Inequalities for a polynomial and its derivative”, Math. Inequal. Appl., 4 (1998), 543–550 | MR | Zbl

[16] Ponnusamy S., Foundations of Complex Analysis, 2nd ed., Narosa Publishing House Pvt. Ltd., 2005 | MR