Continuous Strictly Midpoint-Concave Function is Strictly Concave

Theorem

Let $f$ be a real function which is defined on a real interval $I$.

Let $f$ be strictly midpoint-concave and continuous on $I$.

Then $f$ is strictly concave.

Proof

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Also see

• Continuous Midpoint-Concave Function is Concave

• Continuous Midpoint-Convex Function is Convex
• Continuous Strictly Midpoint-Convex Function is Strictly Convex