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The constant factors in the above five inequalities are all the best possible.
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These two inequalities prove the claim.
Now, the following two inequalities: (2.8).
The above two inequalities yield (53). □.
First, we prove one of two inequalities.
Adding these two inequalities, we have (10).
The two inequalities can be easily produced.
Adding these two inequalities, we get (2.23).
Combining the last two inequalities yields the desired result.
Adding the two inequalities, from (i) we have (2.27).
Adding the last two inequalities, we get that (3.14).
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