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Feb 13, 2023 at 18:34 comment added Iosif Pinelis @user497696 : As I said, this would very much depend on the norm. Also, I think in general there will be no such asymptotic at all, because an arbitrary convex function can behave weirdly in any neighborhood of a given point.
Feb 13, 2023 at 13:39 comment added user497696 Thanks for your answer. However, I am wondering if it is possible to derive a result that $I(M) = V(M) (1 + o(1))$, where $V(M)$ is a certain analytical function? In other words, the small $o(\cdot)$ notation should lie outside the exponent term.
Feb 9, 2023 at 14:56 history answered Iosif Pinelis CC BY-SA 4.0