Hardy-Hilbert's Inequality Research Articles

Upper bounds for Berezin numbers of self-adjoint operators and applications

We prove upper bounds for Berezin symbols and Berezin numbers of operators, with a special emphasis on the quadratic weighted operator geometric mean. In particular, we prove some upper bounds for Berezin symbols and Berezin numbers of some self-adjoint operators on reproducing kernel Hilbert spaces over some suitable sets. Moreover, we estimate the best possible constant in some generalized Hardy-Hilbert inequality for the series.

Gamma-Nabla Hardy–Hilbert-Type Inequalities on Time Scales

We investigated several novel conformable fractional gamma-nabla dynamic Hardy–Hilbert inequalities on time scales in this study. Several continuous inequalities and their corresponding discrete analogues in the literature are combined and expanded by these inequalities. Hölder’s inequality on time scales and a few algebraic inequalities are used to demonstrate our findings.

On Hardy-Hilbert-type inequalities with $ \alpha $-fractional derivatives

<abstract><p>In the current manuscript, new alpha delta dynamic Hardy-Hilbert inequalities on time scales are discussed. These inequalities combine and expand a number of continuous inequalities and their corresponding discrete analogues in the literature. We shall illustrate our results using Hölder's inequality on time scales and a few algebraic inequalities.</p></abstract>

Some New Inequalities Involving the Generalized Hardy Operator

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

Important Study on the ∇ Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert-type on time scales. We present and prove very important generalized results with the help of the Fenchel–Legendre transform, submultiplicative functions, and Hölder’s and Jensen’s inequality on time scales. We obtain some well-known time scale inequalities due to Hardy–Hilbert inequalities. For some specific time scales, we further show some relevant inequalities as special cases: integral inequalities and discrete inequalities. Symmetry plays an essential role in determining the correct methods for solutions to dynamic inequalities

Generalizations of Hardy Type Inequalities by Taylor’s Formula

Abstract In this paper, we use Taylor’s formula to prove new Hardy-type inequalities involving convex functions. We give new results that involve the Hardy–Hilbert inequality, Pólya–Knopp inequality and bounds for the identity related to the Hardy-type functional. At the end, mean value theorems of Cauchy type are given.

A more accurate extended Hardy-Hilbert's inequality with parameters

A more accurate extended Hardy-Hilbert's inequality with parameters

Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications

The main objective of the present article is to prove some new ∇ dynamic inequalities of Hardy–Hilbert type on time scales. We present and prove very important generalized results with the help of Fenchel–Legendre transform, submultiplicative functions. We prove the (γ,a)-nabla conformable Hölder’s and Jensen’s inequality on time scales. We prove several inequalities due to Hardy–Hilbert inequalities on time scales. Furthermore, we introduce the continuous inequalities and discrete inequalities as special case.

On a more accurate Hardy-Hilbert's inequality in the whole plane

By introducing independent parameters and applying the weight coefficients, we use Hermite-Hadamard's inequality and give a more accurate Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a few particular cases and the operator expressions are considered.

ON A NEW HILBERT-TYPE INEQUALITY IN THE WHOLE PLANE WITH THE GENERAL HOMOGENEOUS KERNEL

<abstract> By means of the weight coefficients and the idea of introducing parameters, a new discrete Hilbert -type inequality in the whole plane with the general homogeneous kernel is given, which is an extension of Hardy-Hilbert's inequality. The equivalent form is obtained. The equivalent statements of the best possible constant factor related to several parameters, the operator expressions and a few particular cases are considered. </abstract>

An extended Hardy-Hilbert's inequality with parameters and applications

An extended Hardy-Hilbert's inequality with parameters and applications

Dynamic Hardy-type inequalities with non-conjugate parameters

Within this paper, we derive entire series of new Hilbert and Hardy-Hilbert form integral inequalities with non-conjugate exponents on time scales. Firstly, we demonstrate and discuss two general equivalent inequalities of this type, as well as their corresponding reverse inequalities. We also extend Hilbert and Hardy-Hilbert inequalities in their most general form. The results obtained are then applied to a kernel of special Hardy form. Our results as special cases extend some of the dynamic inequalities achieved on time scales and also include some integral inequalities as special cases when T=R.

ON AN EXTENDED HARDY-HILBERToS INEQUALITY IN THE WHOLE PLANE

By introducing independent parameters and applying the weight coefficients, we give an extended Hardy-Hilbert's inequality in the whole plane with a best possible constant factor. Furthermore, the equivalent forms, a few particular cases and the operator expressions are considered.

A MORE ACCURATE MULTIDIMENSIONAL HARDY-HILBERT'S INEQUALITY

In this paper, by the use of the weight coefficients, the transfer formula, Hermite-Hadamard's inequality and the technique of real analysis, a more accurate multidimensional Hardy-Hilbert's inequality with multiparameters and a best possible constant factor is given, which is an extension of some published results. Moreover, the equivalent forms and the operator expressions are considered.

Hardy-Hilbert's inequality and power inequalities for Berezin numbers of operators

Hardy-Hilbert's inequality and power inequalities for Berezin numbers of operators

A NEW EXTENSION ON THE HARDY-HILBERT INEQUALITY

A new Hardy-Hilbert type integral inequality for double series with weights can be established by introducing a parameter <TEX>${\lambda}$</TEX> (with <TEX>${\lambda}</TEX><TEX>></TEX><TEX>1-\frac{2}{pq}$</TEX>) and a weight function of the form <TEX>$x^{1-\frac{2}{r}}$</TEX> (with <TEX>$r$</TEX> > 1). And the constant factors of new inequalities established are proved to be the best possible. In particular, for case <TEX>$r$</TEX> = 2, a new Hilbert type inequality is obtained. As applications, an equivalent form is considered.

A new generalization of Hardy-Hilbert's inequality with non-homogeneous kernel

Let p > 1 , 1/p + 1/p∗ = 1 , and a = (an)n=1 , b = (bm) ∞ m=1 be two complex sequences. We exhibit the generalization of Hardy-Hilbert’s inequality of the following type: ∑ n,m 1 K(φ1(n),φ2(m))|an||bm| < C ( ∞ ∑ n=1 | an f1(φ1(n)) |p ) 1 p ( ∞ ∑ m=1 | bm f2(φ2(m)) |p ) 1 p∗ , where K : (0,∞)× (0,∞) → (0,∞) , f1, f2,φ1,φ2 : (0,∞) → (0,∞) and C is a suitable constant. We also get several interesting inequalities which generalize many recent results. Mathematics subject classification (2010): 26D15, 47B37.

Generalization of Hardy-Hilbert's Inequality and Applications

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an ap- plication, the reverses, some particular results and their equivalent forms are considered.

New inequalities similar to Hardy-Hilbert's inequality

In this paper, we establish a new inequality similar to Hardy-Hilbert's inequality. As applications, some particular results and the equivalent form are derived. The integral analogues of the main results are also given.

Some new inequalities similar to Hardy-Hilbert's inequality

In this paper we have studied some new inequalities similar to Hardy-Hilbert’s inequality. As applications, we have considered the associated integral inequalities. Mathematics subject classification (2010): 26D15.