content_image/313264.jpg content_image/313263.jpg content_image/313262.jpg content_image/313261.jpg
finite. Therefore, from the inequality (28), we have 

which contradicts (22). 

<img src='content_image/313264.jpg'>

Case 2. τ ≤ 1 . Since the proof is similar to proof of Case 1 , we shall give the sketch of the proof. Dividing inequality (18) by z ( t ) , and then integrating from t − τ to t, it is obtained that 

<img src='content_image/313263.jpg'>

Using the similar arguments in Case 1 , we get that lim inf t →∞ z ( t − τ ) z ( t ) is finite. So, from inequality (29), we have 

which contradicts (21). 

<img src='content_image/313262.jpg'>

Moreover, dividing inequality (18) by z ( t ) , and then integrating from n + 1 − τ to n + 1 , it is obtained that 

<img src='content_image/313261.jpg'>

By using the similar arguments in Case 1 , we get that lim inf n →∞ z ( n + 1 − τ ) z ( t ) is finite. 

