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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

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This condition means that no three distinct points on the function can be co-linear.

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