Show that $f$ is convex in $I$ such that $f(\frac{x+y}{2})<\frac{1}{2}(f(x)+f(y))$

Asked Dec 23 '17 at 19:21

Active Dec 23 '17 at 19:50

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$f$ is continuous in $I$

Show that if $f$ satisfies the condition $f(\frac{x+y}{2})<\frac{1}{2}(f(x)+f(y))$ so it's convex

What I have to show here is $f(k_1y_1+k_2y_2+..k_ny_n)<k_1f(y_1)+k_2f(y_2)+...k_nf(y_n)$ such that $k_1+k_2+...+k_n=1$

The problem is I don't know how to find those coefficients $k$.

edited Dec 23 '17 at 19:50

Bernard

asked Dec 23 '17 at 19:21

user515918

Should i delet my question or just keep it – user515918 Dec 23 '17 at 19:29
@user515918 If you have found out that this question is already answered in another post then why should you keep it? – Math Lover Dec 23 '17 at 19:34

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