Let $f_1,…, f_m$ be quasiconcave functions on a convex subset X on $IR^n$. Let $p_1,…, p_m$ be nonnegative real numbers.
Then, how can I show that $\sum_{i=1}^mp_if_i $ is also quasi concave function?
Similarly, Let $g_1,…, g_m$ be concave functions on a convex subset X on $IR^n$. Let $p_1,…, p_m$ be nonnegative real numbers.
Then, how can I show that $\sum_{i=1}^mp_ig_i $ is also concave function?
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If $f_i$ is quasiconcave then, $\{u,v\}\in$ domain of f for $0<a<1$, and for $f_i(u)> f_i(v)$ $f_i(au+(1-a)v)\ge f_i(v)$
Similarly, for concavitiy, $g_i(au+(1-a)v)\ge ag_i(u)+(1-a)g_i(v)$
And then, how can I proceed the proof?
Thank you. All helps will be appreciated.
*duplicated question