Abstract
In this note we discuss convexity properties of functions f: I→ [−∞,∞[ defined on an interval I⊂ℝ. One of our main results is the following: If the function f: I→ [−∞,∞[ satisfies the convexity inequality for some t∈]0, 1[, then the same holds true for all rational t∈[0, 1].
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References
R. Ger, Homogeneity sets for Jensen-convex functions. General Inequalities 2 (Oberwolfach 1978), 193-201, Internat. Ser.Numer. Math. 47, Birkhäuser, Basel-Stuttgart, 1980.
G. Rodé, Eine abstrakte Version des Satzes von Hahn-Banach. Arch.Math. 31 1978), 474–481.
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© 1984 Springer Basel AG
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Kuhn, N. (1984). A Note on t-Convex Functions. In: Walter, W. (eds) General Inequalities 4. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 71. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6259-2_25
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DOI: https://doi.org/10.1007/978-3-0348-6259-2_25
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-6261-5
Online ISBN: 978-3-0348-6259-2
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