Abstract

CORONEL, ANÍBAL  and  LOZADA, ESPERANZA. A new proof for a Özban conjecture. Integración - UIS [online]. 2021, vol.39, n.2, pp.129-135.  Epub Apr 18, 2022. ISSN 0120-419X.  https://doi.org/10.18273/revint.v39n2-2021001.

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 Ozban ['New algebraic-trigonometric inequalities of Laub-Ilani type', Bull. Aust. Math. Soc. 96 (2017), 87-97] and recently proved by Matejička ['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.

Keywords : Laub-Ilani inequality; trigonometric inequality; algebraic-trigonometric inequality; power-exponential inequality.

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