Spherically symmetric functions with a convex second derivative and applications to extremal probabilistic problems
Document Type
Article
Publication Date
11-1-2002
Department
Department of Mathematical Sciences
Abstract
We describe the class of all functions φ: [0, ∞)→ℝ for which the second derivative gφDdagger;(x; y, y) of the spherically symmetric function gφ(x):= φ(|x|) in the direction of y is convex in x, where x and y are vectors in a Hilbert space H and |·| is the norm in H. Applications to extremal probabilistic problems are given.
Publication Title
Mathematical Inequalities and Applications
Recommended Citation
Pinelis, I.
(2002).
Spherically symmetric functions with a convex second derivative and applications to extremal probabilistic problems.
Mathematical Inequalities and Applications,
5(1), 7-26.
http://doi.org/10.7153/mia-05-02
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/3261