Okay this is what I have for theorem b of the book:
I'm using the explanation for theorem a) in the book (at the bottom of page 54)
f is convex, the set = is convex for every number a
I'm not fully understanding what I'm doing here but here is my answer;
let x and y be points in
Then x and y belong to S
NOTE: [Am i right in saying that x is the f(x) = f(xa...xn) and y is the g(x) = g(x1....xn) in this proof?]
f(x) <= a
f(y) <= a
IF λ [0,1]
then belongs to S
Since S is a convex set...
As f is convex also; (I move now to the definition on page 54 of a convex set)
for all x and y in S and all Lambda in [0,1]
Shows that in all
confirms is convex.....
Is this correct?
Honestly I just changed the words from the proof of part a on page 54, and don't really understand the Theorem
Any help would be much appreciated!