On non-symmetric $t$-convexity

Paolo Leonetti

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arXiv · 2608.00067

On non-symmetric $t$-convexity

Paolo Leonetti

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Abstract

Zsolt P\'ales asked whether there exists a function $f: \mathbb{R}\to \mathbb{R}$ such that $$ f\left(\frac{x+2y}{3}\right) \le \frac{f(x)+2f(y)}{3} \quad \text{ for all }x\le y $$ which is not midconvex. We show that the answer is negative.

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Paolo Leonetti. 2026-07-29. On non-symmetric $t$-convexity. https://arxiv.org/abs/2608.00067

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