Reverse Hilbert-type Inequality Research Articles

Some New Generalizations of Reverse Hilbert-Type Inequalities via Supermultiplicative Functions

Our work in this paper is based on the reverse Hölder-type dynamic inequalities illustrated by El-Deeb in 2018 and the reverse Hilbert-type dynamic inequalities illustrated by Rezk in 2021 and 2022. With the help of Specht’s ratio, the concept of supermultiplicative functions, chain rule, and Jensen’s inequality on time scales, we can establish some comprehensive and generalize a number of classical reverse Hilbert-type inequalities to a general time scale space. In time scale calculus, results are unified and extended. At the same time, the theory of time scale calculus is applied to unify discrete and continuous analysis and to combine them in one comprehensive form. This hybrid theory is also widely applied on symmetrical properties which play an essential role in determining the correct methods to solve inequalities. As a special case of our results when the supermultiplicative function represents the identity map, we obtain some results that have been recently published.

On a New Reverse Hilbert's Type Inequality

In this paper, by using the Euler-Maclaurin expansion for the Riemann-$zeta$ function, we establish an inequality of a weight coefficient. Using this inequality, we derive a new reverse Hilbert's type inequality. As an applications, an equivalent form is obtained.

Some New Generalizations of Reverse Hilbert-Type Inequalities on Time Scales

This manuscript develops the study of reverse Hilbert-type inequalities by applying reverse Hölder inequalities on T. We generalize the reverse inequality of Hilbert-type with power two by replacing the power with a new power β,β>1. The main results are proved by using Specht’s ratio, chain rule and Jensen’s inequality. Our results (when T=N) are essentially new. Symmetrical properties play an essential role in determining the correct methods to solve inequalities.

Some New Reverse Hilbert’s Inequalities on Time Scales

This paper is interested in establishing some new reverse Hilbert-type inequalities, by using chain rule on time scales, reverse Jensen’s, and reverse Hölder’s with Specht’s ratio and mean inequalities. To get the results, we used the Specht’s ratio function and its applications for reverse inequalities of Hilbert-type. Symmetrical properties play an essential role in determining the correct methods to solve inequalities. The new inequalities in special cases yield some recent relevance, which also provide new estimates on inequalities of these type.

On a more accurate reverse Hilbert-type inequality in the whole plane

On a more accurate reverse Hilbert-type inequality in the whole plane

On Reverse Hilbert–Pachpatte-Type Inequalities

In the present paper, we establish some reverse Hilbert-type inequalities which in special case yield some inverses of Pachpatte’s inequalities. Our results provide some new estimates to these types of inequalities.

Reverse Hilbert type inequalities

In this paper we establish a new inverse inequality of Hilbert type for a finite number of positive sequences of real numbers. The integral analogue of the inequality are also proved. The results of this paper reduce to that of B. G. Pachpatte.

Reverse Hilbert inequalities involving series

Some reverse Hilbert's type inequalities involving series of nonnegative terms are established by the use of the technique of real analysis, which provides new estimates on inequalities of these type.

On Generalization of a Reverse Hilbert's Type Inequality

On Generalization of a Reverse Hilbert's Type Inequality

A New Reverse Hilbert's Type Inequality

A New Reverse Hilbert's Type Inequality

A Reverse Hilbert's Type Inequality

In this paper, by using the Euler-Maclaurin expansion, we establish an inequality of a weight coefficient. Using this inequality, we derive a reverse Hilbert's type inequality. As applications, an equivalent form is obtained.

On reverse Hilbert-type inequalities

By introducing two pairs of conjugate exponents and estimating the weight coefficients, we establish reverse versions of Hilbert-type inequalities, as described by Jin (J. Math. Anal. Appl. 340:932-942, 2008), and we prove that the constant factors are the best possible. As applications, some particular results are considered.

A more accurate half-discrete reverse Hilbert-type inequality with a non-homogeneous kernel

A more accurate half-discrete reverse Hilbert-type inequality with a non-homogeneous kernel

On a half-discrete reverse Hilbert-type inequality

By using the weight functions and the techniques of real analysis, a half-discrete reverse Hilbert-type inequality with the best constant factor is given. A best extension with a parameter λ and the equivalent forms are also considered.

A reverse Hilbert-type inequality with a generalized homogeneous kernel

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

A reverse Hilbert-type inequality with a generalized homogeneous kernel

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

A reverse Hilbert-type inequality with a generalized homogeneous kernel

Inthispaper,by introducing a generalized homogeneous kernel and estimating the weight function,a new reverse Hilbert-type integral inequality with some parameters and a best constant factor is established.Furthermore, the corresponding equivalent form is considered.

Extension of reverse Hilbert-type inequality with some parameters

By introducing some parameters and estimating the weight function, we obtain an extension of reverse Hilbert-type inequality with the best constant factor. As applications, we build its equivalent forms and some particular results.

A new reverse Hilbert-type inequality with a best constant factor

In this paper, we give a new reverse Hilbert-type inequality with a best constant factor and some parameters. As application, we consider the equivalent form and some particular results.