Convex optimisation constitutes a fundamental area in applied mathematics where the objective is to identify the minimum of a convex function subject to a set of convex constraints. This framework ...

Let X be a reflexive Banach space and let Ф be an extended real-valued lower semicontinuous convex function on X. Given a real A and the sublevel set S = [Ф ≤ λ], we establish at x̅ ϵ S the following ...

Matrix inequalities and convex functions constitute a central theme in modern mathematical analysis, with far‐reaching implications across numerical analysis, optimisation, quantum information, and ...

We show that a Banach space is a Grothendieck space if and only if every continuous convex function on X has a continuous biconjugate function on X**, thus also answering a question raised by S.