Note on a quadratic inequality

Peter Renaud
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 30, 2024, Number 3, Pages 587–589
DOI: 10.7546/nntdm.2024.30.3.587-589
Full paper (PDF, 144 Kb)

Details

Authors and affiliations

Peter Renaud
School of Mathematics and Statistics, University of Canterbury
Christchurch, New Zealand

Abstract

In this note we obtain a quadratic inequality based on a result of Atanassov but in a more symmetric form. Somewhat surprisingly, well-known properties of Chebyshev polynomials can be used to give a straightforward proof.

Keywords

• Inequalities
• Chebyshev polynomials of the second kind

2020 Mathematics Subject Classification

• 11A25

References

1. Atanassov, K. (2012). A modification of an elementary numerical inequality. Notes on Number Theory and Discrete Mathematics, 18(3), 5–7.
2. Beran, L., & Novakova, E. (1998). On an inequality of Atanassov. The Australian Mathematical Society Journal, 25(5), 235–235.
3. Coope, I., & Renaud, P. (1999). A quadratic inequality of Atanassov. The Australian Mathematical Society Journal, 26(4), 169–170.
4. Mason, J. C., & Handscomb, D. C. (2003). Chebyshev Polynomials. Chapman and Hall/CRC.

Manuscript history

• Received: 8 February 2024
• Revised: 4 October 2024
• Accepted: 16 October 2024
• Online First: 21 October 2024

Copyright information

Ⓒ 2024 by the Author.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).