Sandwich theorem for reciprocally strongly convex functions
Abstract 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.
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| Auteurs principaux: | , , |
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| Format: | Digital revista |
| Langue: | English |
| Publié: |
Universidad Nacional de Colombia y Sociedad Colombiana de Matemáticas
2018
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| Accès en ligne: | http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S0034-74262018000200171 |
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