Let be a semialgebraic function , . Shiota (1986) proved that given a positive continuous semialgebraic function , there is a semialgebraic function such that  for every . In this talk, we show that the theorem still holds if we replace semialgebraic functions by definable functions in polynomially bounded o-minimal structures that allow smooth cell decompositions. Some applications are also given. This is a joint work with Anna Valette.