New posts in Jensen Inequality

Proof that if $x,y>0$ and $x+y=1$, then $(2x)^{\frac 1 x}+(2y)^{\frac 1 y}\leq 2$

If $f'' \ge 0$, $\int_0^2 f(x)dx \ge 2f(1)$

Prove that $\sum \frac{x}{x^2+7}\le \frac{3}{8}$

An inequality for polynomials with positives coefficients

Prove that $\left ( 1+\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}+\left ( 1-\frac{n^{\frac{1}{n}}}{n} \right )^\frac{1}{n}<2$

Nice olympiad inequality :$\frac{xy^2}{4y^3+3}+\frac{yz^2}{4z^3+3}+\frac{zx^2}{4x^3+3}\leq \frac{3}{7}$

Inequality : $\Big(\frac{x^n+1+(\frac{x+1}{2})^n}{x^{n-1}+1+(\frac{x+1}{2})^{n-1}}\Big)^n+\Big(\frac{x+1}{2}\Big)^n\leq x^n+1$

tangent inequality in triangle

Maximum value of expression $a+b+c$

A conjecture about power sum : $e^{ab}+e^{bc}+e^{ca}\geq 3e^{\sqrt{abc}}$ and $a+b+c=3$