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Results tagged with convexity
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user 18827
For questions involving the concept of convexity
3
votes
1
answer
582
views
Concavity of the solution of a parametric implicit function
Suppose $F(x,y;k)=f(x,y)+kg(x,y)=0$ uniquely defines the solution $y(x;k)$ for $x\in \mathbb{D}$, a compact domain, and $0\leq k \leq 1$ is a parameter. We know that for $k=0,1$, $y(x;0)$ and $y(x,1)$ …
- 141
2
votes
0
answers
214
views
When can sublinear growth imply concavity?
Consider a function $f(x,\lambda):\mathbb{R}^{2}_{+}\to\mathbb{R}_{+}$ that is uniformly continuous, smooth, lower bounded and convex. Let
$\qquad g(\lambda)=\inf_{x}\;f(x,\lambda)$
We know that $g( …
- 141