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If x = 1 and x = 2, then from our theorems we can deduce the conclusions of [4, 5].

Since (6.3) implies that L n + p − 1 − 1 m > 0 and λ n > 0, we can deduce the conclusions (6.4) similarly as in Lemma 2.2.

If x = 1, b = 1 (respectively, x = 2, b = 1 ) or x = 1, b = 3, then from our theorems we can deduce the conclusions of [7 10], and [11].

We then deduce the conclusion from Theorem 3.1.

By Lemmas 5.3 5.4 we can deduce the conclusion as follows.

We can deduce the conclusion directly from the definition.

Then we deduce the conclusion of this lemma.

Once this is established, the Brouwer theorem will be invoked to deduce the conclusion.

end{aligned} Thus, combining (14), (38), and (39), we deduce the conclusion (2).

By these facts, we can deduce the conclusion of Theorem 2.9.