Stability of a negative feedback amplifier
"I read in the text book that if fp &lt; fg, for the frequency between fp and fg, the amplifier is not stable."

Please, can you quote the relevant part of the textbook? This sentence sounds as if the author thinks, that the amplifier could be unstable for some certain input frequencies only ("between fp and fg").  

Here is my answer: If a system with feedback does not fulfill the stability criterion (negative phase margin and/or gain margin), it will be unstable and either oscillate or go into saturation. This effect is independent on the frequency of the input signal. Rather, it is an effect of self-excitement.