Abstract
Let D ⊂ ℝN be a convex and open set, and let f : D → ℝ be a convex function. Let m f be the lower hull of f (cf. 6.3). By Theorem 6.3.1 either mf (x) = -∞ for all x ∈ D, or mf : D → ∝ is a continuous and convex function.
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© 2009 Birkhäuser Verlag AG
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(2009). Further Properties of Additive Functions and Convex Functions. In: Gilányi, A. (eds) An Introduction to the Theory of Functional Equations and Inequalities. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8749-5_12
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DOI: https://doi.org/10.1007/978-3-7643-8749-5_12
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8748-8
Online ISBN: 978-3-7643-8749-5
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