Solution-Find the convex function, Generalize the above

Find the convex function

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Reference no: EM13891098

(a) Show that if f : R → R and g : R → R are convex functions then max{f, g} is also a convex function.

(b) Generalize the above result to show that if {fi; i ∈ I} is a family of convex functions and supi ∈ I fi(x) ∞ for every x then supi∈I fi is also a convex function.

Conclude that if H : R → R is a function then there exists the largest convex function G such that G(x) ≤ H(x) for every x.

Reference no: EM13891098

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Find the convex function

Reference no: EM13891098

Reference no: EM13891098

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