Jensen’s inequality

For a convex function $f$ and points $\mathbf{x}^{(1)},…,\mathbf{x}^{(t)}$, $$f\left(\frac{1}{t}\cdot\mathbf{x}^{(1)}+...+\frac{1}{t}\cdot\mathbf{x}^{(t)}\right) \leq \frac{1}{t}\cdot$$

More generally, deriving from Variance and Expectation, $\mathbb{E}[f(X)] \geq f(\mathbb{E}[X])$

For concave function,

References:

1. https://www.probabilitycourse.com/chapter6/6_2_5_jensen's_inequality.php
2. https://mathworld.wolfram.com/JensensInequality.html