👉 Learn how to determine the differentiability of a function. A function is said to be differentiable if the derivative ...

👉 Learn how to find the value that makes a function continuous. A function is said to be continuous if two conditions are ...

Given x 0 , a point of a convex subset C of a Euclidean space, the two following statements are proven to be equivalent: (i) every convex function f : C → ℝ is upper semi-continuous at x 0 , and (ii) ...

Given a separated dual system (E, E'), the Fenchel transform determines a pairing of the convex functions on E with the convex functions on E'. This operation is shown to have a continuity property.