Convexity of set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0

Main Question or Discussion Point

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

Answers and Replies

7
0
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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