9.1 If xi,yi, i = 1,2,…,l, are real numbers, then prove the Cauchy-Schwarz inequality:
9.2 Prove that the ℓ2 (Euclidean) norm is a true norm, that is, it satisfies the four conditions that define a norm.
9.3 Prove that any function that is a norm is also a convex function.
9.4 Show Young’s inequality for nonnegative real numbers a and b,
for and such that
9.5 Prove Holder’s inequality for