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arXiv · 2510.03715

Jensen convex functions and doubly stochastic matrices

Matyas Barczy·Zsolt Páles
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Abstract

Given an nxn doubly stochastic matrix P satisfying an appropriate condition of linear algebraic-type, and a function f defined on a nonempty interval, we show that the validity of a convexity-type functional inequality for f in terms P implies that f is Jensen convex. We also prove that if f is convex, then the functional inequality in question holds for all doubly stochastic matrices of any order. The particular case when the doubly stochastic matrix is a circulant one is also considered.

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Matyas Barczy, Zsolt Páles. 2025-10-04. Jensen convex functions and doubly stochastic matrices. https://arxiv.org/abs/2510.03715

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