u of

In this case, P < As,. = aP2'Y = Ao, "f < Asn+l = aP~ = A1 and a < Asn+2 = a 2 P'Y = A2 for all n 2:: 0. This implies that

and so

Assume (a) holds. Take

and

Now assume (b) holds.

%2 = <4)2/J =a. and so, Eq.(1) has a prime period 3 solution. 0

Throughout this section, we will assume An = A for all n ~ 0. Theorem 5. Comider Eq.(7) where A E (O,oo) and the initial conditiom Z-1 and zo are arbitrafll po1itiue number~- Then the following ltatementl are tnle.