Category:Convex Real Functions
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This category contains results about Convex Real Functions.
Definitions specific to this category can be found in Definitions/Convex Real Functions.
$f$ is convex on $I$ if and only if:
- $\forall x, y \in I: \forall \alpha, \beta \in \R_{>0}, \alpha + \beta = 1: \map f {\alpha x + \beta y} \le \alpha \map f x + \beta \map f y$
Also see
Subcategories
This category has the following 4 subcategories, out of 4 total.
Pages in category "Convex Real Functions"
The following 28 pages are in this category, out of 28 total.
C
- Conditional Jensen's Inequality
- Convex Real Function Composed with Increasing Convex Real Function is Convex
- Convex Real Function is Continuous
- Convex Real Function is Left-Hand and Right-Hand Differentiable
- Convex Real Function is Measurable
- Convex Real Function is Pointwise Supremum of Affine Functions
E
I
- Inverse of Strictly Decreasing Convex Real Function is Convex
- Inverse of Strictly Decreasing Strictly Convex Real Function is Strictly Convex
- 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