BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS

Mahboobeh Shamoradi; Mahmood Bidkham

BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS

Abstract

Considering a class of polynomials ${\small G(z) = a_n z^n +\sum\limits_{v=t}^{n} a_{n-v}z^{n-v}, 1\leq t \leq n}$ having all it's zeros in the disk $|z|\leq k$, $k\leq 1$, we present a generalization and improvement of results by Malik and Vong[8]. Also a variety of interesting results emerge as special cases of our findings.

Keywords

Thanks

The authors wish to sincerely thank the referees, for the careful reading of the paper and for the helpful suggestions and comments.

References

Aziz, A., (1987), Growth of polynomials whose zeros are within or outside a circle, Bulletin of the Australian Mathematical Society, 35(2),pp. 247-256.
Aziz, A. and Dawood, Q.M., (1988), Inequalities for a polynomial and its derivative, Journal of Approximation Theory, 54(3), pp. 306-313.
Aziz, A. and Rather, N. A., (2004), Some compact generalization of Bernstien-type inequalities for polynomials, Mathematical Inequalities and Applications, 7(3), pp. 393 - 403 .
Aziz, A. and Shah, M., (2004), Inequalities for a polynomial and its derivative, Mathematical Inequalities and Applications, 7 (3), pp. 379–391.
Bernstein, S., (1930), Sur la limitation des dérivées des polynomes, C. R.. Acad. Sc. Paris, 190, pp. 338–340.
Dewan, K. K. and Hans, S., (2010), Generalization of certain well-known polynomial inequalities, Journal of Mathematical Analysis and Applications, 363, 38-41.
Malik, M. A., (1969), On the Derivative of a Polynomial, Journal of the London Mathematical Society,1(s2), pp. 57–60.
Malik, M. A. and Vong, M.C., (1985), Inequalities concerning the derivative of polynomials , Rendiconti del Circolo Matematico di Palermo, 34(3), pp. 422-426.

Details

Primary Language

English

Subjects

Real and Complex Functions (Incl. Several Variables)

Journal Section

Research Article

Authors

Mahboobeh Shamoradi This is me
0009-0008-0334-4745
Iran

Mahmood Bidkham ^* This is me
0000-0002-3048-3635
Iran

Publication Date

March 17, 2026

Submission Date

February 14, 2025

Acceptance Date

June 23, 2025

Published in Issue

Year 2026 Volume: 16 Number: 3

IZ

https://izlik.org/JA95SM72DG

Cite

RIS / Bibtex

APA

Shamoradi, M., & Bidkham, M. (2026). BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS. TWMS Journal of Applied and Engineering Mathematics, 16(3), 341-348. https://izlik.org/JA95SM72DG

AMA

1.Shamoradi M, Bidkham M. BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS. JAEM. 2026;16(3):341-348. https://izlik.org/JA95SM72DG

Chicago

Shamoradi, Mahboobeh, and Mahmood Bidkham. 2026. “BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS”. TWMS Journal of Applied and Engineering Mathematics 16 (3): 341-48. https://izlik.org/JA95SM72DG.

EndNote

Shamoradi M, Bidkham M (March 1, 2026) BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS. TWMS Journal of Applied and Engineering Mathematics 16 3 341–348.

IEEE

[1]M. Shamoradi and M. Bidkham, “BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS”, JAEM, vol. 16, no. 3, pp. 341–348, Mar. 2026, [Online]. Available: https://izlik.org/JA95SM72DG

ISNAD

Shamoradi, Mahboobeh - Bidkham, Mahmood. “BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS”. TWMS Journal of Applied and Engineering Mathematics 16/3 (March 1, 2026): 341-348. https://izlik.org/JA95SM72DG.

JAMA

1.Shamoradi M, Bidkham M. BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS. JAEM. 2026;16:341–348.

MLA

Shamoradi, Mahboobeh, and Mahmood Bidkham. “BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 3, Mar. 2026, pp. 341-8, https://izlik.org/JA95SM72DG.

Vancouver

1.Mahboobeh Shamoradi, Mahmood Bidkham. BERNSTEIN-TYPE INEQUALITIES FOR COMPLEX POLYNOMIALS. JAEM [Internet]. 2026 Mar. 1;16(3):341-8. Available from: https://izlik.org/JA95SM72DG