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, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals time scale calculus. These extensions used to generalize Hardy-type inequalities with general kernels variables. Some Hardy Hilbert Polya Knop type also discussed as special cases. Classical new deduced from main results using particular scales.

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.

This study shows that a refinement of the Hilbert inequality for double series can be established by introducing a real function u x and a parameter λ. In particular, some sharp results of the classical Hilbert inequality are obtained by means of a sharpening of the Cauchy inequality. As applications, some refinements of both the Fejer-Riesz inequality and Hardy inequality inHp function are given.

where the constant factor [π/ sin(π/p)]p is also the best possible. Hardy-Hilbert inequalities are important in analysis and in their applications (see [7]). In recent years, many results (see [1, 3, 8–10]) have been obtained in the research of Hardy-Hilbert inequality. At present, because of the requirement of higher-dimensional harmonic analysis and higher-dimensional operator theory, multipl...

In this paper we derive new inequalities involving the generalized Hardy operator. The obtained results known We also get classical Hardy–Hilbert inequality.

In this paper, by introducing some parameters and by employing a sharpening of Hölder’s inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder’s theorem is given.

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 extended Hardy–Hilbert’s inequality with multi-parameters. Then, obtain equivalent forms some statements best possible constant factor related several parameters. Finally, illustrate how obta...

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.