The local slope operator was introduced in De Giorgi et al.(Atti Accad Naz Lincei Rend Cl
Sci Fis Mat Nat 68: 180–187, 1980) to study gradient flow dynamics in metric spaces. This …

The norm of the gradient‖∇ f (x)‖ measures the maximum descent of a real-valued
smooth function f at x. For (nonsmooth) convex functions, this is expressed by the distance …

A classical result of variational analysis, known as Attouch theorem, establishes an
equivalence between epigraphical convergence of a sequence of proper convex lower …

We show that the deviation between the slopes of two convex functions controls the
deviation between the functions themselves. This result reveals that the slope—a one …

We study the fundamental properties of pointwise semi-Lipschitz functions between
asymmetric spaces, which are the natural asymmetric counterpart of pointwise Lipschitz …

In the first part of the seminar, we will revise some literature concerning determination
results. The determination result of Rockafellar for convex functions [13], the determination …

Abstract In 2018, Boulmezaoud, Cieutat and Daniilidis [1] obtained a very unexpected
determination result: For any two convex functions f, g over a Hilbert space H, that are of …

The fundamental theorem of calculus asserts that, for every two differentiable functions f, g:
Rn→ R one has that∇ f (x)=∇ g (x),∀ x∈ Rn=⇒ f= g+ c, for some constant c∈ R. This is …