On a multidimensional half-discrete Hilbert-type inequality related to the hyperbolic cotangent function

On Hardy-type integral inequalities in the whole plane related to the extended Hurwitz-zeta function

“…Furthermore, Hong [10] considered as well an equivalent condition between a Hilbert-type inequality with homogenous kernel and a few parameters. Some additional kinds of Hilbert-type inequalities were also obtained in [11][12][13][14][15][16][17][18][19]. Most of these results are constructed in the quarter plane of the first quadrant.…”

Equivalent properties of a Mulholland-type inequality with a best possible constant factor and parameters

“…Observe that (17) keeps the form of equality if and only if there exist constants A and B such that they are not all zero and (cf. [26])…”

“…Some extensions of (4) were provided in [14][15][16][17][18][19]. In 2016, by using the techniques of real analysis, Hong [20] considered some equivalent statements of the general form of (1) with the homogeneous kernel related to a few parameters and a best possible constant factor.…”

A Half-Discrete Hardy-Hilbert-Type Inequality with a Best Possible Constant Factor Related to the Hurwitz Zeta Function

“…With the assumptions of Theorem 1, if there exists n 0 ∈ N, such that v n ≥ v n+1 (n ∈ {n 0 , n 0 + 1, · · · }), and U(∞) = V (∞) = ∞, then the constant factor k(σ ) in (22), (23) and (24) is the best possible.…”