Maximum Modulus of the Derivatives of a Polynomial with Zeros Outside a Circle

Authors

  • Reingachan Ngamchui National Institute of Technology Manipur, India
  • Nirmal Kumar Singha National Institute of Technology Manipur and The Assam Royal Global University, India
  • Barchand Chanam National Institute of Technology Manipur, India

DOI:

https://doi.org/10.7546/CRABS.2026.08.01

Keywords:

polynomial, zero, maximum modulus, s-th derivative, Gauss–Lucas theorem

Abstract

In this paper, we present higher-order derivative extensions of a result established by Aziz and Mohammad [Proc. Amer. Math. Soc., 81 (1981), 549–553], thereby encompassing several known results as particular cases. In addition, a detailed numerical example along with graphical analysis is provided to demonstrate the accuracy and sharpness of the proposed results.

Author Biographies

Reingachan Ngamchui, National Institute of Technology Manipur, India

Mailing Address:
Department of Mathematics,
National Institute of Technology Manipur,
Langol 795004, India

E-mail: reinga14@gmail.com

Nirmal Kumar Singha, National Institute of Technology Manipur and The Assam Royal Global University, India

Mailing Addresses:
Department of Mathematics,
National Institute of Technology Manipur,
Langol 795004, India
and
Department of Mathematics,
The Assam Royal Global University,
Guwahati 781035, India

E-mails: nirmalsingha99@gmail.com,
nksingha@rgu.ac

Barchand Chanam, National Institute of Technology Manipur, India

Mailing Address:
Department of Mathematics,
National Institute of Technology Manipur,
Langol 795004, India

E-mail: barchand_2004@yahoo.co.in

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Published

25-08-2026

How to Cite

[1]
R. Ngamchui, N. Singha, and B. Chanam, “Maximum Modulus of the Derivatives of a Polynomial with Zeros Outside a Circle”, C. R. Acad. Bulg. Sci., vol. 79, no. 8, pp. 1013–1021, Aug. 2026.

Issue

Vol. 79 No. 8 (26)

Section

Mathematics

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