A Note on Hilbert Type Inequality

Pachpatte, B. G.

doi:10.5556/j.tkjm.29.1998.4258

Cited by 33 publications

(9 citation statements)

References 5 publications

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“…where rm i = m i m i 1 and M (k; r) = 1 2 p kr: In the same paper [7], an integral version of (2) is established in the next consequence. If 2 C 1 ([0; x); R) ; !…”

Section: Introductionmentioning

confidence: 86%

Generalization of dynamic Hilbert-Pachpatte inequality via Taylor formula on time scale

El-Owaidy

Mohamed

El‐Deeb

et al. 2023

Preprint

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“…where rm i = m i m i 1 and M (k; r) = 1 2 p kr: In the same paper [7], an integral version of (2) is established in the next consequence. If 2 C 1 ([0; x); R) ; !…”

Section: Introductionmentioning

confidence: 86%

Generalization of dynamic Hilbert-Pachpatte inequality via Taylor formula on time scale

El-Owaidy

Mohamed

El‐Deeb

et al. 2023

Preprint

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show abstract

“…In [10], Pachappte established a discrete Hilbert-type inequality and its integral version, as in the following two theorems: Theorem 9. Let {a m }, {b n } be two nonnegative sequences of real numbers defined for m = 1, .…”

Section: Theoremmentioning

confidence: 99%

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

2022

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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

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“…where the coefficient t is best possible. In [28], Pachappte established a discrete Hilbert-type inequality and its integral version as in the following two theorems: Theorem 13. Let {a m }, {b n } be two nonnegative sequences of real numbers defined for m = 1, .…”

Section: Definitionmentioning

confidence: 99%

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

El‐Deeb

Awrejcewicz

2021

Mathematics

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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.

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A Note on Hilbert Type Inequality

Abstract: In the present note we establish a new Hilbert type inequality mvolving sequences of real numbers. An integral analogue of the main result is also given.

Cited by 33 publications

References 5 publications

Generalization of dynamic Hilbert-Pachpatte inequality via Taylor formula on time scale

Generalization of dynamic Hilbert-Pachpatte inequality via Taylor formula on time scale

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

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

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