New posts in Jensen Inequality

Prove that $({a\over a+b})^3+({b\over b+c})^3+ ({c\over c+a})^3\geq {3\over 8}$

Prove that $(1+x)^\frac{1}{x}+(1+\frac{1}{x})^x \leq 4$

Prove that $E(e^{X}) < \frac{1}{2}(e^{-K} + e^{K})$ if $E(X)=0$ and $|X|<K$ almost surely

Prove that $\int_E \log fd\mu \leqslant \mu(E) \, \log \left[\frac{1}{\mu(E)} \right]$ for strictly positive measure $\mu$

$(a+2)^3+(b+2)^3+(c+2)^3 \ge 81$ while $a+b+c=3$

Prove that $\sum \limits_{cyc}\frac {a}{(b+c)^2} \geq \frac {9}{4(a+b+c)}$

Prove that $xy \leq\frac{x^p}{p} + \frac{y^q}{q}$

If $a+b+c+d=16$, then $(a+\frac{1}{c})^2+(c+\frac{1}{a})^2 + (b+\frac{1}{d})^2 + (d+\frac{1}{b})^2 \geq \frac{289}{4}$