New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

El‐Deeb, Ahmed A.; Rashid, Saima; Khan, Zareen A.; Makharesh, Samer D.

doi:10.1186/s13662-021-03394-w

Cited by 2 publications

(2 citation statements)

References 40 publications

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“…Over several decades, Hilbert-type inequalities have attracted many researchers and several refinements, and the previous results have been extended. We refer the reader to the works on classical refinements and extensions of Hilbert-type inequalities [12][13][14][15][16][17][18][19][20][21][22] and time scale versions of Hilbert-type inequalities [23][24][25][26]. ([14]).…”

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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Section: Theoremmentioning

confidence: 99%

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

2022

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“…Over several decades Hilbert-type inequalities have been attracted many researchers and several refinements and extensions have been done to the previous results, we refer the reader to the works [15][16][17][18][19][20][21][22][23][24][25][26].…”

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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New dynamic Hilbert-type inequalities in two independent variables involving Fenchel–Legendre transform

Cited by 2 publications

References 40 publications

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

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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