Convexity of a function I don't understand

[newphysist]

Hi,

I am starting to learn real math I would say for first time in life. I have come across this function:

f(x) = max[SUB]i[/SUB](x[SUB]i[/SUB]) - min[SUB]i[/SUB](x[SUB]i[/SUB])

The domain is R.

Does the above function mean f(x) = 0 since for for x in R max and min of x would be x itself.

Hence it is convex as for any θ ≥ 0 we can write:

θ.x + (1-θ).y = 0 ≤ f(θ.x + (1-θ).y)
f(θ.x + (1-θ).y) = 0

In above both x and y would be any R.

Thanks for helping me learn.

 

[Yuu Suzumi]

Is the argument of $f$ perhaps a vector and the $x_i$ the components thereof? I am sure they are not meant to be the same.