By improving an inequality of the weight coefficient, we give a new strengthened version of Hardy-Hilbert’s type inequality. As its applications, we build some strengthened versions of the equivalent form and some particular results.

By introducing some parameters and the weight coefficient, one proves a new extension of the Hilbert-type inequality with a best constant factor. The reverse, some equivalent forms and a number of new particular cases are considered.

In this paper it is shown that a new Hardy-Hilbert type integral inequality can be established by introducing a proper integral kernel function, and that the constant factor is proved to be the best possible. In particular, for case p = 2, a new Hilbert type integral inequality is given .And as the mathematics aesthetics, several important constants π and Euler number En appear simultaneously i...

Abstract By the use of weight coefficients, idea introduced parameters and technique real analysis, a more accurate Hilbert-type inequality in whole plane with general homogeneous kernel is given, which an extension Hardy–Hilbert’s inequality. An equivalent form obtained. The statements best possible constant factor related to several parameters, operator expressions few particular cases are co...

By means of the weight functions, the technique of real analysis and Hermite-Hadamard's inequality, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of logarithmic function and a best possible constant factor is given. Moreover, the equivalent forms, the operator expressions, the reverses and some particular cases are also considered.

By means of weight functions and Hermite-Hadamard's inequality, and introducing a discrete interval variable, a more accurate half-discrete Hardy-Hilbert-type inequality related to the kernel of arc tangent function and a best possible constant factor is given, which is an extension of a published result. The equivalent forms and the operator expressions are also considered.

In this paper, by using the way of weight function and real analysis techniques, a new integral inequality with some parameters and a best constant factor is given, which is a relation to Hilbert’s integral inequality and some base Hilbert-type integral inequalities. The equivalent form and the reverse forms are considered.

Making use of weight coefficients as well real/complex analytic methods, an extension a Hardy–Hilbert-type inequality with best possible constant factor and multiparameters is established. Equivalent forms, reverses, operator expression the norm, few particular cases are also considered.

Abstract In this paper, by virtue of the symmetry principle, applying techniques real analysis and Euler–Maclaurin summation formula, we construct proper weight coefficients use them to establish a reverse Hardy–Hilbert inequality with power function as intermediate variables. Then, obtain equivalent forms some statements best possible constant factor related several parameters. Finally, illust...