Sandwich theorem for reciprocally strongly convex functions

Mireya Bracamonte; José Giménez; Jesús Medina

doi:10.15446/recolma.v52n2.77157

Publicado

2018-07-01

Sandwich theorem for reciprocally strongly convex functions

Teorema del Sandwich para funciones fuerte-recíprocamente convexas

DOI:

https://doi.org/10.15446/recolma.v52n2.77157

Palabras clave:

Convex functions, Sandwich theorem, Hyers-Ulam (en)
Funciones convexas, Teorema del Sandwich, Hyers-Ulam (es)

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Autores/as

Mireya Bracamonte Escuela Superior Politécnica del Litoral (ESPOL)
José Giménez Universidad de Los Andes
Jesús Medina Universidad Centroccidental Lisandro Alvarado

Resumen (en)
Resumen (es)

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.

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.

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Cómo citar

APA

Bracamonte, M., Giménez, J. y Medina, J. (2018). Sandwich theorem for reciprocally strongly convex functions. Revista Colombiana de Matemáticas, 52(2), 171–184. https://doi.org/10.15446/recolma.v52n2.77157

ACM

[1]

Bracamonte, M., Giménez, J. y Medina, J. 2018. Sandwich theorem for reciprocally strongly convex functions. Revista Colombiana de Matemáticas. 52, 2 (jul. 2018), 171–184. DOI:https://doi.org/10.15446/recolma.v52n2.77157.

ACS

(1)

Bracamonte, M.; Giménez, J.; Medina, J. Sandwich theorem for reciprocally strongly convex functions. rev.colomb.mat 2018, 52, 171-184.

ABNT

BRACAMONTE, M.; GIMÉNEZ, J.; MEDINA, J. Sandwich theorem for reciprocally strongly convex functions. Revista Colombiana de Matemáticas, [S. l.], v. 52, n. 2, p. 171–184, 2018. DOI: 10.15446/recolma.v52n2.77157. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/77157. Acesso em: 24 abr. 2024.

Chicago

Bracamonte, Mireya, José Giménez, y Jesús Medina. 2018. «Sandwich theorem for reciprocally strongly convex functions». Revista Colombiana De Matemáticas 52 (2):171-84. https://doi.org/10.15446/recolma.v52n2.77157.

Harvard

Bracamonte, M., Giménez, J. y Medina, J. (2018) «Sandwich theorem for reciprocally strongly convex functions», Revista Colombiana de Matemáticas, 52(2), pp. 171–184. doi: 10.15446/recolma.v52n2.77157.

IEEE

[1]

M. Bracamonte, J. Giménez, y J. Medina, «Sandwich theorem for reciprocally strongly convex functions», rev.colomb.mat, vol. 52, n.º 2, pp. 171–184, jul. 2018.

MLA

Bracamonte, M., J. Giménez, y J. Medina. «Sandwich theorem for reciprocally strongly convex functions». Revista Colombiana de Matemáticas, vol. 52, n.º 2, julio de 2018, pp. 171-84, doi:10.15446/recolma.v52n2.77157.

Turabian

Bracamonte, Mireya, José Giménez, y Jesús Medina. «Sandwich theorem for reciprocally strongly convex functions». Revista Colombiana de Matemáticas 52, no. 2 (julio 1, 2018): 171–184. Accedido abril 24, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/77157.

Vancouver

1.

Bracamonte M, Giménez J, Medina J. Sandwich theorem for reciprocally strongly convex functions. rev.colomb.mat [Internet]. 1 de julio de 2018 [citado 24 de abril de 2024];52(2):171-84. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/77157

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2. Mea Bombardelli, Sanja Varošanec. (2023). Strongly MφMψ -Convex Functions, The Hermite–Hadamard–Fejér Inequality and Related Results. Annales Mathematicae Silesianae, https://doi.org/10.2478/amsil-2023-0019.

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