int_U fV(h(u)g(u))du>=fV(int_U h(u)g(u)du) what if the function f is not convex but concave - f_C

Uriah Molina

Uriah Molina

Answered question

2022-11-11

U f V ( h ( u ) g ( u ) ) d u f V ( U h ( u ) g ( u ) d u )
what if the function f is not convex but concave - f C .

Answer & Explanation

hamputlnf

hamputlnf

Beginner2022-11-12Added 12 answers

Hint: f ( x ) is convex if and only if f ( x ) is concave.
If
f ( Ω g ( x ) d μ ( x ) ) Ω f ( g ( x ) ) d μ ( x )
then negating both sides, we get
f ( Ω g ( x ) d μ ( x ) ) Ω f ( g ( x ) ) d μ ( x )

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