Solution
= Solution
A <strictly convex function> satisfies the strict inequality
$$
\boxed{F((1-t)x+ty)<(1-t)F(x)+tF(y)
\quad\text{if }x\ne y,\ 0<t<1.}
$$
Endpoint and coincident-point cases are excluded because they necessarily give equality.
= Solution
A <strictly convex function> satisfies the strict inequality
$$
\boxed{F((1-t)x+ty)<(1-t)F(x)+tF(y)
\quad\text{if }x\ne y,\ 0<t<1.}
$$
Endpoint and coincident-point cases are excluded because they necessarily give equality.