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

peteryellow

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

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