Una nueva prueba para una conjetura de Özban

• Autores: Aníbal Coronel, Esperanza Lozada
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 39, Nº. 2, 2021, págs. 129-135
• Idioma: español
• DOI: 10.18273/revint.v39n2-2021001
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    En este artículo presentamos una prueba corta y elemental de la siguiente desigualdad algebraico-trigonométrica de tipo Laub-Ilani: cos(xy) + cos(yx) ≥ cos(xx) + cos(yy) para x, y ∈ [0, π/2] que fue conjeturada por Özban [‘New algebraic-trigonometric inequalities of Laub-Ilani type’, Bull. Aust. Math. Soc. 96 (2017), 87–97] y recientemente probada por Matejíčka [‘Proof of one open inequality of Laub-Ilani type’, Journal of Mathematical Inequalities, 14 (2020), 83–98]. La prueba se basa en las propiedades de las funciones potenciales-exponenciales y trigonométricas.

  • English

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

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