In this paper functions f:(a,b)→R are considered with the property that for all n>2 and all x1,x2,...,xn∈(a,b) is convex in k. Functions with this property are called sequentially convex. It is proved that if f is convex, twice differentiable, and f″ is convex then f is sequentially convex. In case f is a continous function defined on the whole ofR these conditions are necessary too.
KeywordsNumber Theory Algebraic Geometry Topological Group Continous Function
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- BOAS, R. P., Jr. and D. V. WIDDER: Functions with positive differences. Duke math. J. 7, 496–503 (1940)Google Scholar
- CARLSON, B. C., MEANY, R. K. and S. A. NELSON: Mixed arithmetic and geometric means. Pacific J. Math. 38 343–349 (1971)Google Scholar
- POPOVICIU, T.: Les fonctions convexes. Paris: Hermann 1944Google Scholar
- POPOVICIU, T.: sur certaines inégalités qui caractérisent les fonctions convexes. An. Sti. Univ. Al. I Cuza Iasi, n. Ser., Sect. Ia 11B, 155–164 (1965)Google Scholar
- ROBERTS, A. W. and D. E. VARBERG: Convex Functions. New York and London: Academic Press 1973Google Scholar
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