INEQUALITY'S BLOG

August 1, 2010

Problem 040

Filed under: Uncategorized — KKKVVV @ 7:26 am

Let f:R\longrightarrow R_{0}^{+} and f''>0. For a, b, c be positive real numbers and satisfying a\leq b\leq c. Prove that:

\displaystyle \frac{a^2f(b)}{b+c}+\frac{b^2f(c)}{c+a}+\frac{c^2f(a)}{a+b}\geq \frac{abf(c)}{c+a}+\frac{bcf(a)}{a+b}+\frac{caf(b)}{b+c}

 

Van Khea    

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