Geodesic
Growth of a polynomial not vanishing in a disk
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 73 (2019) no. 1, pp. 41-48 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

This paper deals with the problem of finding some upper bound estimates for the maximum modulus of the derivative and higher order derivatives of a complex polynomial on a disk under the assumption that the polynomial has no zeros in another disk. The estimates obtained strengthen the well-known inequality of Ankeny and Rivlin about polynomials.
Keywords: Polynomial, maximum modulus principle, zeros 
@article{AUM_2019_73_1_a1,
     author = {Mir, Abdullah},
     title = {Growth of a polynomial not vanishing in a disk},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica},
     pages = {41--48},
     year = {2019},
     volume = {73},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a1/}
}
TY  - JOUR
AU  - Mir, Abdullah
TI  - Growth of a polynomial not vanishing in a disk
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica
PY  - 2019
SP  - 41
EP  - 48
VL  - 73
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a1/
LA  - en
ID  - AUM_2019_73_1_a1
ER  - 
%0 Journal Article
%A Mir, Abdullah
%T Growth of a polynomial not vanishing in a disk
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica
%D 2019
%P 41-48
%V 73
%N 1
%U http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a1/
%G en
%F AUM_2019_73_1_a1
Mir, Abdullah. Growth of a polynomial not vanishing in a disk. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 73 (2019) no. 1, pp. 41-48. http://geodesic.mathdoc.fr/item/AUM_2019_73_1_a1/

[1] Ankeny, N. C., Rivlin, T. J., On a theorem of S. Bernstein, Pacific J. Math. 5 (1955), 849–852.

[2] Aziz, A., Aliya, Q., Growth of polynomials not vanishing in a disk of prescribed radius, Int. J. Pure Appl. Math. 41 (2007), 713–734.

[3] Govil, N. K., Qazi, M. A., Rahman, Q. I., Inequalities describing the growth of polynomials not vanishing in a disk of prescribed radius, Math. Ineq. Appl. 6 (2003), 453–467.

[4] Jain, V. K., A generalization of Ankeny and Rivlin’s result on the maximum modulus of polynomials not vanishing in the interior of the unit circle, Turk. J. Math. 31 (2007), 89–94.

[5] Milovanovic, G. V., Mitrinovic, D. S., Rassias, Th. M., Topics in polynomials, Extremal problems, Inequalities, Zeros, World scientific, Singapore, 1944.