Alsina, Claudi 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 Keywords:Jensen inequality; continuous Jensen-convex functions Citations:Zbl 0573.00004 PDFBibTeX XML