Is the following restatement of convexity wrong?

Question

They claim equation 5 is restatement of convexity. What am I missing? $\lambda = 0, \lambda'=1$ seems wrong no?

https://www.scihive.org/paper/1702.04877

Answer 1

Take $F(x) = x$ on the reals, $p=0,q=1, \lambda = 1, \lambda' = 1$ then the above says $F(q)=1 \le F(p) = 0$.