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Sandwich theorem for reciprocally strongly convex functions
Teorema del Sandwich para funciones fuerte-recíprocamente convexas
DOI:
https://doi.org/10.15446/recolma.v52n2.77157Palabras clave:
Convex functions, Sandwich theorem, Hyers-Ulam (en)Funciones convexas, Teorema del Sandwich, Hyers-Ulam (es)
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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.
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.
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Derechos de autor 2018 Revista Colombiana de Matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.