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.

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) ...

<span class=author>ER KUNAL</span><br />Differential calculus:Burning topics: Different types of function and its periodicity, limit and continuity of a function ...

Real numbers, limits, continuity, differentiability, mean-value theorems, Taylor's theorem with remainders, indeterminate forms, maxima and minima, asyptotes ...