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?]

Continuing:

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!