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Results tagged with convexity
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user 43628
For questions involving the concept of convexity
2
votes
1
answer
187
views
When is a continuous subadditive function (0,1]-superhomogeneous
Continuous version of this Superhomogeneity of subadditive functions
Let $f$ be a continuous function of $\geq 2$ real variables defined on a convex cone $\mathcal{C}$ in the upper half plane, with $f …
- 128k
2
votes
1
answer
108
views
Superhomogeneity of subadditive functions
Let $f$ be a function of $\geq 2$ real variables defined on a convex cone $\mathcal{C}$ in the upper half plane, with $f(0) = 0$. Suppose $f$ is subadditive, i.e. $f(x_1+y_1, \dots,
x_n+y_n) \leq f(x …
- 128k
0
votes
1
answer
80
views
Planar function inequality on parallelograms
Let $f$ be a function defined on the unit square $R = [0,1]^2 \subseteq \mathbf{R}^2$ which is convex and satisfies $\frac{\partial{f}^2 }{\partial{x}\partial{y}} \leq 0$. The last condition is equiva …
