# What is the significance of strictly convex?

I am learning the definition of convex (in a book on information theory). The book says that that if equality holds only when $$λ$$ is 0 or 1 then the function is "strictly" convex.

$$f(\lambda x+(1−\lambda)y)\leq \lambda f(x)+(1−\lambda)f(y)$$

I have a good Intuition behind convex functions. But I don't understand the significance behind "strict" convexity. I understand how linear functions could be convex and how, for a linear function, the equality would hold when $$λ$$ has any value. Is "strict" convexity meant to exclude such cases? This question seems to get to the same problem but does not answer my question: Visual difference between strictly concave and not strictly concave