New posts in functional-inequalities

Can we show that the determinant of this matrix is non-zero?

Weighted Poincare Inequality

Solve $f (x + y) + f (y + z) + f (z + x) \ge 3f (x + 2y + 3z)$

An upper bound of binary entropy

How prove this function inequality $xf(x)>\frac{1}{x}f\left(\frac{1}{x}\right)$

Are there (known) bounds to the following arithmetic / number-theoretic expression?

Prove that $\int_0^1|f''(x)|dx\ge4.$

Does this inequality hold true, in general?

prove a challenging inequality or find a counterexample to it

If $f(x)\leq f(f(x))$ for all $x$, is $x\leq f(x)$?

Deducing Inequality from an Equation

What is the maximum value of $\frac{2x}{x + 1} + \frac{x}{x - 1}$, if $x \in \mathbb{R}$ and $x > 1$?

If $f$ is continuous and $\,f\big(\frac{1}2(x+y)\big) \le \frac{1}{2}\big(\,f(x)+f(y)\big)$, then $f$ is convex [duplicate]