On maximum modulus for the derivative of a polynomial
K. Dewan ; Sunil Hans
Annales UMCS, Mathematica, Tome 63 (2009), p. 55-62 / Harvested from The Polish Digital Mathematics Library

If P(z) is a polynomial of degree n, having all its zeros in the disk [...] then it was shown by Govil [Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546] that [...] In this paper, we obtain generalization as well as improvement of above inequality for the polynomial of the type [...] Also we generalize a result due to Dewan and Mir [Southeast Asian Bull. Math. 31 (2007), 691-695] in this direction.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:268104
@article{bwmeta1.element.doi-10_2478_v10062-009-0006-x,
     author = {K. Dewan and Sunil Hans},
     title = {On maximum modulus for the derivative of a polynomial},
     journal = {Annales UMCS, Mathematica},
     volume = {63},
     year = {2009},
     pages = {55-62},
     zbl = {1190.30003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0006-x}
}
K. Dewan; Sunil Hans. On maximum modulus for the derivative of a polynomial. Annales UMCS, Mathematica, Tome 63 (2009) pp. 55-62. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_v10062-009-0006-x/

Bernstein, S., Lecons sur les propriétés extrémales et la meilleure approximation desfonctions analytiques d'une variable réelle, Gauthier Villars, Paris, 1926. | Zbl 52.0256.02

Dewan, K. K., Mir, A., Note on a theorem of S. Bernstein, Southeast Asian Bull. Math. 31 (2007), 691-695. | Zbl 1150.30001

Govil, N. K., On the derivatives of a polynomial, Proc. Amer. Math. Soc. 41, no. 2 (1973), 543-546. | Zbl 0279.30004

Govil, N. K., On a theorem of S. Bernstein, J. Math. Phys. Sci., 14, no. 2 (1980), 183-187. | Zbl 0444.30007

Govil, N. K., Some inequalities for derivatives of polynomials, J. Approx. Theory 66 (1991), 29-35. | Zbl 0735.41006

Govil, N. K., Rahman, Q. I., Functions of exponential type not vanishing in a half plane and related polynomials, Trans. Amer. Math. Soc. 137 (1969), 501-517. | Zbl 0189.08502

Pólya, G., Szegö, G., Problems and Theorems in Analysis, Vol. 1, Springer-Verlag, New York, 1972. | Zbl 0236.00003

Qazi, M. A., On the maximum modulus of polynomials, Proc. Amer. Math. Soc. 115 (1992), 337-343. | Zbl 0772.30006

Turán, P., Über die ableitung von Polynomen, Compositio Math. 7 (1939), 89-95. | Zbl 65.0324.01