Iterative process, with CDF solving

I need to solve when this converges, and my intial guess is c, how do i code this? The CDF of u can be anything simple.

c=4.427
L1=248.5197399
L2=0.503968457
B=0.998
gamma=0.310366941
u1=c/L1+B*((1-L2)/(1-B*L2))*(u+(1-F(u))*gamma)