content_image/295848.jpg content_image/295847.jpg content_image/295846.jpg content_image/295845.jpg content_image/295844.jpg content_image/295843.jpg
to t, it is obtained that 

<img src='content_image/295848.jpg'>

where P ( t ) is defined in (15). Since e x ≥ ex for x ∈ R , we obtain that 

Let u ( t ) = z ( t − 1) z ( t ) . Since z ( t ) is nonincreasing for t > T , lim inf t →∞ u ( t ) ≥ 1 . 

Assume that lim inf t →∞ u ( t ) = + ∞ . Then integrating inequality (14) from t − 1 2 to t, we have t 

Since z ( t ) is nonincreasing, from the above inequality, we obtain that 

Dividing inequality (25) by z ( t ) and z ( t − 1 $_{2}$) , we get 

and 

<img src='content_image/295847.jpg'>

<img src='content_image/295846.jpg'>

<img src='content_image/295845.jpg'>

<img src='content_image/295844.jpg'>

<img src='content_image/295843.jpg'>

