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Hence, we get assertion.

From these inequalities and part (b) of the RC-conditions we get assertion 1.

Using the same proof method as in Theorem 1, we get assertion of Theorem 2.

Hence, we get the assertion.

end{aligned} Then we get the assertion (31).

collecting the above estimate, we get the assertion.

Thus from (3.13) and (3.20) we get the assertion.

By Theorem 2 again, we get the assertion.

Then, by above relation and by virtue of Theorem 3, we get the assertion.

(2.19) Substituting (2.19) in (2.17), we get the assertion of this lemma.

By the positive definiteness of the matrix S, we get the assertion (32).