A. Daniilidis

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20242026

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math.FA2026

A convexity criterion via the De Giorgi slope

Tahar Z. Boulmezaoud, Aris Daniilidis, TrÃ Minh LÃª

Let $X$ be a Banach space and $f \in C^{1} (X)$ be bounded from below. We show that if for some $m \geq 1$ , the function $x \mapsto ∥\nabla f (x) ∥^{m}$ is convex, then $f$ is con…

math.FA2025

Determination of (unbounded) convex functions via Crandall-Pazy directions

Aris Daniilidis, David Salas, SebastiÃ¡n Tapia-GarcÃa

It has been recently discovered that a convex function can be determined by its slopes and its infimum value, provided this latter is finite. The result was extended to nonconvex f…

math.FA2024

ABB theorems: Results and limitations in infinite dimensions

Aris Daniilidis, Carlo de Bernardi, Enrico Miglierina

We construct a weakly compact convex subset of $ℓ^{2}$ with nonempty interior that has an isolated maximal element, with respect to the lattice order $ℓ_{+}^{2}$ . Moreover, the ma…