Definition: Here a neighborhood of the point c → ∈ R n is the set...
Definition: Here a neighborhood of the point is the set for some , and a subset is said to be convex if implies .
My Attempt: Suppose and , we then have and . Now,
My Question: How should I make less than ? My intuition is that I need the Cauchy-Schwarz inequality; but I am unsure where to apply it. Any hint would be greatly appreciated.