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-   -   Convexity of set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0 (http://www.physicsforums.com/showthread.php?t=222715)

peteryellow Mar18-08 09:34 AM

Convexity of set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0
 
How can I show that the set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0 y>=0} is convex.

CHatUPenn Mar21-08 11:41 PM

I am sure it can be shown by definition, but I propose an easy way (not rigorous though)

The function is (weakly) convex
The lower contour set (=<1) of a convect function is convex.


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