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ZHU Pengxian (2017).
Management Science and Engineering, 11 (1), 1-8
Therefore,
Let
that
to see that
Together with (4), this allow us to conclude that
(8)
with t'1<t'2 and θ>0 such
. It is easy
Let τ > 0 be small enough, we have that
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and it follows from (H4) that
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Here, we have used the continuity of T(t) for t > 0 in the uniform operator topology. Therefore, one gets for each
k=0,...,m that
uniformly for
.
Now, we consider the case when t=tk,k=1,...,m. Fix δ2>0 such that
one has
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Also,
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