Abstract
We derive a strengthenment of a Hardy-Hilbert type inequality by using the Euler-Maclaurin expansion for the zeta function and estimating the weight function effectively. As applications, some particular results are presented.MSC:26D15.
Highlights
Let p, q > p + q =, an, bn ≥ < ∞ n= apn
By introducing a parameter and two pairs of conjugate exponents, Zhong gave a generalization of inequality ( . ) with the best constant factor as follows: If p >
By introducing a parameter and estimating the weight coefficient, we obtain a strengthenment of inequality ( . ) and generalize inequality ( . )
Summary
Where the constant factor π sin(π /p) and pq are best possible. ) is named a Hardy-Hilbert type inequality. Many results about generalizations of this type of inequality were established (see [ ]). ), some Hardy-Hilbert type inequalities, which are similar to
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