Abstract
We apply the technique of generalized reduced modules in the proof of some inequalities for polynomials. Various estimates of the module of the derivative are obtained in terms of the module of the polynomial, of its leading coefficient, of the distribution of zeros, or of images of critical points. Bibliography: 9 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
P. Borwein and T. Erdelyi, Polynomials and Polynomial Inequalities, New York (1995).
A. I. Kostrikin, Introduction to Algebra. Foundations of Algebra[in Russian], Moscow (1994).
V. N. Dubinin, “Reduced modules of open sets in the theory of analytic functions," Dokl. Ros. Akad. Nauk, 363, 731-734 (1998).
A. Aziz and N. A. Rather, “L pinequalities for polynomials," Glasnik Mat., 32(52), 39-43 (1997).
V. K. Jain, “Generalization of certain well-known inequalities for polynomials," Glasnik Mat., 32(52), 45-51 (1997).
A. Aziz and N. A. Rather, “A refinement of a theorem of Paul Turan concerning polynomials," Math. Inequal. Appl., 1, 231-238 (1998).
V. N. Dubinin, “Asymptotics of the module of a degenerate condenser and some of their applications," Zap. Nauchn. Semin. POMI, 237, 56-73 (1997).
V. N. Dubinin and L. V. Kovalev, “Reduced module of the complex sphere," Zap. Nauchn. Semin. POMI, 254, 76-94 (1998).
G. Pólya and G. Szego, Isoperimetric Inequalities in Mathematical Physics[Russian translation], Moscow (1962).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dubinin, V.N., Kim, V.Y. Reduced Modules and Inequalities for Polynomials. Journal of Mathematical Sciences 110, 3070–3077 (2002). https://doi.org/10.1023/A:1015468127306
Issue Date:
DOI: https://doi.org/10.1023/A:1015468127306