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Revista Colombiana de Matemáticas
versão impressa ISSN 0034-7426
Rev.colomb.mat. vol.52 no.2 Bogotá jul./dez. 2018
https://doi.org/10.15446/recolma.v52n2.77157
Original articles
Sandwich theorem for reciprocally strongly convex functions
Teorema del Sandwich para funciones fuerte-recíprocamente convexas
1 Escuela Superior Politécnica del Litoral (ESPOL) Departamento de Matemáticas, Facultad de Ciencias Naturales y Matemática, Km 30.5 Vía Perimetral, Campus Gustavo Galindo, Guayaquil, Ecuador. e-mail: mirebrac@gmail.com
2 Universidad de los Andes, Departamento de Matemáticas, Facultad de Ingeniería. Mérida, Venezuela. e-mail: jgimenez@ula.ve
3 Universidad Centroccidental Lisandro Alvarado, Departamento de Matemáticas, Decanato de Ciencias y Tecnología. Barquisimeto, Venezuela. e-mail: jesus.medina@ucla.edu.ve
We introduce the notion of reciprocally strongly convex functions and we present some examples and properties of them. We also prove that two real functions f and g, defined on a real interval [a, b], satisfy
for all x, y ∈ [a, b] and t ∈ [0, 1] iff there exists a reciprocally strongly convex function h: [a, b] → R such that f (x) ≤ h(x) ≤ g(x) for all x ∈ [a, b].
Finally, we obtain an approximate convexity result for reciprocally strongly convex functions; namely we prove a stability result of Hyers-Ulam type for this class of functions.
Keywords: Convex functions; Sandwich theorem; Hyers-Ulam
En este artículo introducimos la noción de funciones recíproca-fuertemente convexas y presentamos algunos ejemplos y propiedades. Además se demuestran que dos funciones f y g, definidas en el intervalo real [a, b] satisfacen la desigualdad
para todo x, y ∈ [a, b] y t ∈ [0, 1] si, y sólo si, existe una función recíproca-fuertemente convexa h : [a, b] → R tal que f (x) ≤ h(x) ≤ g (x) para todo x ∈ [a, b].
Finalmente, se obtiene un resultado de aproximación convexa para esta clase de funciones.
Palabras clave: Funciones convexas; Teorema del Sandwich; Hyers-Ulam
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Received: January 31, 2018; Accepted: May 08, 2018
This is an open-access article distributed under the terms of the Creative Commons Attribution License
