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Results tagged with inequalities
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user 75701
for questions involving inequalities, upper and lower bounds.
1
vote
Accepted
Lower bound for $ \sum_{i=1}^n x_i f(x_i)$ when $\sum_{i=1}^{n}x_i = K$
Actually,the conclusion is negative.
By chebyshev's theorem, we have
$$
\sum_{i=1}^{n}{x_{i}\cdot f(x_{i})}\geq \frac{\sum_{i}^{n}{f(x_{i} ) } }{n} \times \sum_{1}^{n}{x_{i} }
$$
$$
\forall x_{1}< …
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