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

  1. How can I show that the set A = {(x,y) in R^2 | x^4+y^4 =< 1, x>=0 y>=0} is convex.
  2. jcsd
  3. 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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