Let the function f(x) be defined on the interval i. If there are any two points x 1 and x2 in I, and any λ∈(0, 1), then there are both.

f(λx 1+( 1-λ)x2)& lt； =λf(x 1)+( 1-λ)f(x2)，

If the inequality is strictly established, that is, "

If "=" is a convex function. Similarly, there are strictly convex functions.

Let f(x) be continuous on the interval d if it is constant for any two points A and B on d.

f((a+b)/2)& lt； (f(a)+f(b))/2

Then the graph of f(x) on d is (upward) concave (or concave arc); If there is.

f((a+b)/2)>(f(a)+f(b))/2

Then the graph of f(x) on d is convex (or convex arc).