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.
CBSE Class 12 Mathematics Chapter 5 Continuity and Differentiability Revision Notes: With the 2024 board exams around the corner, the time to put down the books and begin revising the concepts has ...
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) ...
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