# Category:Concave Real Functions

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This category contains results about Concave Real Functions.

$f$ is **concave on $I$** if and only if:

- $\forall x, y \in I: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: f \left({\alpha x + \beta y}\right) \ge \alpha f \left({x}\right) + \beta f \left({y}\right)$

## Also see

## Pages in category "Concave Real Functions"

The following 17 pages are in this category, out of 17 total.

### C

### E

### I

- Inverse of Strictly Decreasing Concave Real Function is Concave
- Inverse of Strictly Decreasing Strictly Concave Real Function is Strictly Concave
- Inverse of Strictly Increasing Concave Real Function is Convex
- Inverse of Strictly Increasing Convex Real Function is Concave
- Inverse of Strictly Increasing Strictly Concave Real Function is Strictly Convex
- Inverse of Strictly Increasing Strictly Convex Real Function is Strictly Concave