content_image/311031.jpg content_image/311032.jpg content_image/311034.jpg content_image/311033.jpg content_image/311035.jpg content_image/311037.jpg content_image/311036.jpg
Thus, for s ∈ ( $^{s$_{k}$$_{0}$}$− $_{1}$, s$_{k}$$_{0}$$_{+2}$$_{E}$ ] , we have that 

<img src='content_image/311031.jpg'>

Let us define the functions u ( s ) = e λs ∥ φ$_{ζ}$ ( s ) − φ$_{˜}$ $_{ζ}$( s ) ∥ and v ( s ) = β$_{1}$ + β$_{2}$e $^{λs}$, where 

and 

One can confirm by means of (4.9) that 

<img src='content_image/311032.jpg'>

<img src='content_image/311034.jpg'>

<img src='content_image/311033.jpg'>

It can be shown by applying the analogue of the Gronwall’s Lemma for piecewise continuous functions that 

Accordingly, the inequality 

is valid. Therefore, 

<img src='content_image/311035.jpg'>

<img src='content_image/311037.jpg'>

<img src='content_image/311036.jpg'>

