Korean J. Math. Vol. 31 No. 1 (2023) pp.55-61
DOI: https://doi.org/10.11568/kjm.2023.31.1.55

A generalization of an inequality concerning the Smirnov operator

Main Article Content

Ishrat Ul Fatima Bhat
Wali Mohammad Shah


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

Supporting Agencies

Science and Engineering Research Board, Govt. of India under Mathematical Research Impact-Centric Sport(MATRICS) Scheme vide SERB Sanction


[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