Geodesic
Exponential convexity and total positivity
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 802-806 Cet article a éte moissonné depuis la source Math-Net.Ru

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Class of exponentially convex functions is a sub-class of convex functions on a given interval $(a, b)$. For exponentially convex function $f(x)$ S. N. Bernstein's integral representation holds. A condition for $f(x)$, providing the kernel $K(x, y)=f(x+y)$ to be totally positive is given. New examples of totally positive kernels are obtained. For example the kernel $(x+y)^{-\alpha}$ is totally positive for any $\alpha > 0$.
Keywords: exponential convexity, total positivity
Mots-clés : kernel. 
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N. O. Kotelina; A. B. Pevny. Exponential convexity and total positivity. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 17 (2020), pp. 802-806. http://geodesic.mathdoc.fr/item/SEMR_2020_17_a132/

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