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smidsol04 - 4 Let f and g be convex functions on a convex...

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Unformatted text preview: 4. Let f and g be convex functions on a convex set S. Define-a function h by ' h(z) = rf(x) + sg(w) for all x in S, Where 7" and 5 are positive real numbers. Prove that h is also a convex ( function on S, making it clear in your ‘proof how you are making use of the hypothesis that r and s are positive. jm‘u log 71 C/ml/Qfi diznlvM/U 05“.l M 1,763 ...
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