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Using Lemma 2.1, we immediately obtain (2.28).

Thus, by (3.2), we immediately obtain that.

From (3.21), we immediately obtain inequality (1.11).

Then by (3.5), we immediately obtain the inequality (3.13).

Combining inequality (4.11) with (3.8), we immediately obtain inequality (4.8).

From this, we immediately obtain lim n → ∞ I ( n ) = 0.

Letting in (2.69), we immediately obtain the desired inequality (2.53).

Therefore, we immediately obtain the following regularity result.

By setting for all, we immediately obtain the result.

By the above analysis, we immediately obtain the following.

Therefore, by Theorem 2.5, from (3.14), we immediately obtain (3.11).