ABSTRACT

Observe that if z 2: 0 , then zO'o = zO' , while if z < 0 , then zO'o = _( _ z)O' . We begin by considering the question of existence of solutions in the class M+ . Theorem 1 . If for all No E N we have

(Cd

Proof. Assume that ( 1 ) has a solution {Yn } E M+ , say, Yn > 0 , ll.Yn 2: 0 , Yo(n) > 0 , and ll.Yo(n ) 2: 0, for all n � Nl for some integer Nl � No . The proof for a negative solution is similar and will be omitted . From ( 1 ) , we have

and from condition (Cd, we have

This contradicts ll.Yn � 0 for all n 2: Nl and completes the proof of the theorem.