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From mid-point to full convexity. (English) Zbl 0586.26005

General inequalities 4, Mem. E. F. Beckenbach, 4th Int. Conf., Oberwolfach/Ger. 1983, ISNM 71, 399 (1984).
[For the entire collection see Zbl 0573.00004.]
The fact that all continuous Jensen-convex functions are convex is proved without Cauchy \((2\to 2^ n\to 2^ n-k)\) induction.
Reviewer: J.Aczél

MSC:

26A51 Convexity of real functions in one variable, generalizations
26D15 Inequalities for sums, series and integrals

Citations:

Zbl 0573.00004