For any function f and its convex conjugate f * Fenchel's inequality (also known as the Fenchel–Young inequality) holds for every x ∈ X and p ∈ X *, i.e., independent x, p pairs, ⟨ p , x ⟩ ≤ ≤ f ( x ) + f ⋆ ⋆ ( p ) .