Korean J. Math. Vol. 30 No. 2 (2022) pp.231-238
DOI: https://doi.org/10.11568/kjm.2022.30.2.231

Inequalities for a polynomial whose zeros are within or outside a given disk

Main Article Content

Lubna Wali Shah
Mohd Yousf Mir
Wali Mohammad Shah


In this paper we prove some results by using a simple but elegant techniques to improve and strengthen some generalizations and refinements of two widely known polynomial inequalities and thereby deduce some useful corollaries.

Article Details

Supporting Agencies

DST-INSPIRE Fellowship


[1] Abdul Aziz, A refinement of an inequality of S. Bernstein, J. Math. Anal. Appl., 142 (1989), 1– 10. Google Scholar

[2] S. Bernstein, Sur la limitation des d ́eriv ́ees des polynomes, C. R. Acad. Sci. Paris., 190 (1930), 338–340. Google Scholar

[3] C. Frappier, Q. I. Rahman and St. Rusheweyh, New Inequalities for polynomials, Trans. Amer. Math. Soc., 288 (1985), 69–99. Google Scholar

[4] V. N. Dubinin, Applications of the Schwarz Lemma to inequalities for entire functions with constraints on zeros, J. Math. Sci.,(N.Y) 143 (3) (2007), 3069–3076. Google Scholar

[5] V. N. Dubinin, Distortion theorems for polynomials on the circle, Sbornik: Mathematics, 191 (12) (2000), 1797–1807. Google Scholar

[6] P. D. Lax, Proof of a conjecture of P. Erd ̈os on the derivative of a polynomial, Bull. Amer. Math. Soc., 50 (1944), 509–513. Google Scholar

[7] M. A. Malik, On the derivative of Polynomial, J. London Math. Soc., 1 (1969), 57–60. Google Scholar

[8] P. Tura ́n, Uber die Ableitung von Polynomen, Compositio Math., 7 (1939), 89–95. Google Scholar

[9] S. L. Wali and W. M. Shah, Some applications of Dubinin’s lemma to rational functions with prescribed poles, J. Math. Anal. Appl., 450 (2017), 769–779. Google Scholar