Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 39 No. 2 (2021): Revista Integración, temas de matemáticas
Research and Innovation Articles

A new proof for a Özban conjecture

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  • Aníbal Coronel,
  • Esperanza Lozada
Aníbal Coronel
Universidad del Bío-Bío, Departamento de Ciencias Básicas, Chillán, Chile.
Esperanza Lozada
Universidad del Bío-Bío, Departamento de Ciencias Básicas, Chillán, Chile.
DOI: https://doi.org/10.18273/revint.v39n2-2021001

Published 2021-09-27

Keywords

  • Laub-Ilani inequality,
  • trigonometric inequality,
  • algebraictrigonometric inequality,
  • power-exponential inequality

How to Cite

Coronel, A., & Lozada, E. (2021). A new proof for a Özban conjecture. Revista Integración, Temas De matemáticas, 39(2), 129–135. https://doi.org/10.18273/revint.v39n2-2021001

Copyright (c) 2021 Revista Integración, temas de matemáticas

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

In this paper, we present an elementary short proof of the following algebraic-trigonometric inequality of Laub-Ilani type: cos(xy)+cos(yx) ≥ cos(xx) + cos(yy) for x, y ∈ [0, π/2] which was conjectured by Özban [‘New algebraic-trigonometric inequalities of Laub-Ilani type’, Bull. Aust. Math. Soc. 96 (2017), 87–97] and recently proved by Matejíčka [‘Proof of one open inequality of Laub-Ilani type’, Journal of Mathematical Inequalities, 14 (2020), 83–98]. The proof is based on the properties of the power-exponential and trigonometric functions.

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