  The Feigenbaum-Kadanoff-Shenker (FKS) equation is a nonlinear iterative
functional equation, which characterizes the quasiperiodic route to chaos for
circle maps. Instead of FKS equation, we put forward the second type of FKS
equation. We use the iterative construction method to obtain a new kind of
continuous solutions with platforms for this functional equation. We show some
properties of these continuous solutions, and give one relationship of some
solutions between FKS equation and the second type of FKS equation.
