A generalization of an inequality concerning the Smirnov operator
Main Article Content
Abstract
In this paper we establish a generalization of a result recently proved by Ganenkova and Starkov [J. Math. Anal. Appl., 476 (2019), 696-714] concerning a modified version of Smirnov operator.
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.
Supporting Agencies
References
[1] A. Aziz and B. A. Zargar, Inequalities for a polynomial and its derivative, Math. Inequl. Appl. 1 (4) (1998), 543–550. Google Scholar
[2] S. N. Bernstein, Sur l’ordre de la meilleure approximation des fonctions continues par des polynˆomes de degre ́ donn ́e, Memoires de l’Academie Royals de Belgique 4 (1912), 1–103. Google Scholar
[3] S. Bernstein, Sur la limitation des derivees des polynomes, C. R. Acad. Sci. Paris., 190 (1930), 338–340. Google Scholar
[4] E. G. Ganenkova and V. V. Starkov, Variations on a theme of the Marden and Smirnov operators, differential inequalities for polynomials, J. Math. Anal. Appl. 476 (2019), 696–714. Google Scholar
[5] M. Marden, Geometry of polynomials, American Mathematical Soc. 3 (1949). Google Scholar
[6] Q. I. Rahman and G. Schmeisser, Analytic theory of polynomials, Oxford Clarendon Press, (2002). Google Scholar
[7] V. I. Smirnov and N. A. Lebedev, Constructive theory of functions of a complex variable, (Nauka, Moscow,1964) [Russian]. Google Scholar