Abstract
Let D ⊂ ℝN be a convex and open set. In 5.3 we saw that a convex function f : D → ℝ fulfills the inequality
for all x,y ∈ D and all λ ∈ ℚ ∩ [0, 1]. It was also pointed out that if, moreover, f is continuous, then inequality (7.1.1) holds actually for all real λ ∈ [0, 1].
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© 2009 Birkhäuser Verlag AG
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(2009). Continuous 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_7
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DOI: https://doi.org/10.1007/978-3-7643-8749-5_7
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8748-8
Online ISBN: 978-3-7643-8749-5
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