We derive whole series of new integral inequalities of the Hardy-type, with non-conjugate exponents. First, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. General results are then applied to special Hardy-type kernel and power weights. Also, some estimates of weight functions and constant factors are obtained. ...

in this paper, we reconstruct the hardy-littlewood’s inequality byusing the method of the weight coefficient and the technic of real analysis includinga best constant factor. an open problem is raised.

We give a new Hilbert-type integral inequality with the best constant factor by estimating the weight function. And the equivalent form is considered.

Abstract In this work, by the introduction of some parameters, a new half-discrete kernel function in whole plane is defined, which involves both homogeneous and nonhomogeneous cases. By employing techniques real analysis, especially method weight function, Hilbert-type inequality with as well its equivalent Hardy-type inequalities are established. Moreover, it proved that constant factors newl...

Hilbert and Hardy-Hilbert type inequalities see 1 are very significant weight inequalities which play an important role in many fields of mathematics. Although classical, such inequalities have attracted the interest of numerous mathematicians and have been generalized in many different ways. Also the numerous mathematicians reproved them using various techniques. Some possibilities of generali...

By using the methods of weight functions and Hermite-Hadamard’s inequality, two kinds of more accurate equivalent reverse multidimensional half-discrete Hilbert-type inequalities with the kernel of hyperbolic cotangent function are given. The constant factor related to the Riemann zeta function is proved to be the best possible. Mathematics subject classification (2010): 26D15, 47A07, 37A10.

In this paper, we address Hardy–Hilbert-type inequality by virtue of constructing weight coefficients and introducing parameters. By using the Euler–Maclaurin summation formula, Abel’s partial differential mean value theorem, a new weighted containing two sums can be proven, which is further generalization an existing result. Based on obtained results, provide equivalent statements best possibl...