New posts in Functional Inequalities

Is this monotonicity property equivalent to convexity?

Find all continuous functions such that $f(x)f(2x)\dots f(nx) \le an^k$

How can I prove $\log_2{(1+x)} \geq {x}$ for $0<x<1$

Find $f$ such that $(f(x))^2 \ge f(x + y)(f(x) + y), \forall x, y$

An inequality in positive real continuous function

An upper bound of binary entropy

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