How to express nearly convex function in terms of Hessian?

Question

A function $f:R^2\rightarrow R$ is called nearly convex if for any two points $x,y\in R^2$ there exists $t\in (0,1)$ such that $$f((1-t)x+ty)\leq (1-t)f(x)+tf(y).$$ We know that if a function is convex then its Hessian is positive semidefinite. But how can we express the nearly convex function in terms of Hessian?