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 <inline-formula><math xm...

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Autores principales:	Ahmed A. El-Deeb, Jan Awrejcewicz
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	Hardy–Hilbert’s inequality Hölder’s and Jensen’s inequality time scale Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/6af47572d05d44499c9708ea4447fc18
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spelling	oai:doaj.org-article:6af47572d05d44499c9708ea4447fc182021-11-25T18:17:37ZNovel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications10.3390/math92229642227-7390https://doaj.org/article/6af47572d05d44499c9708ea4447fc182021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2964https://doaj.org/toc/2227-7390The 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>γ</mi><mo>,</mo><mi>a</mi><mo>)</mo></mrow></semantics></math></inline-formula>-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.Ahmed A. El-DeebJan AwrejcewiczMDPI AGarticleHardy–Hilbert’s inequalityHölder’s and Jensen’s inequalitytime scaleMathematicsQA1-939ENMathematics, Vol 9, Iss 2964, p 2964 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Hardy–Hilbert’s inequality Hölder’s and Jensen’s inequality time scale Mathematics QA1-939
spellingShingle	Hardy–Hilbert’s inequality Hölder’s and Jensen’s inequality time scale Mathematics QA1-939 Ahmed A. El-Deeb Jan Awrejcewicz Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
description	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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>γ</mi><mo>,</mo><mi>a</mi><mo>)</mo></mrow></semantics></math></inline-formula>-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.
format	article
author	Ahmed A. El-Deeb Jan Awrejcewicz
author_facet	Ahmed A. El-Deeb Jan Awrejcewicz
author_sort	Ahmed A. El-Deeb
title	Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
title_short	Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
title_full	Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
title_fullStr	Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
title_full_unstemmed	Novel Fractional Dynamic Hardy–Hilbert-Type Inequalities on Time Scales with Applications
title_sort	novel fractional dynamic hardy–hilbert-type inequalities on time scales with applications
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/6af47572d05d44499c9708ea4447fc18
work_keys_str_mv	AT ahmedaeldeeb novelfractionaldynamichardyhilberttypeinequalitiesontimescaleswithapplications AT janawrejcewicz novelfractionaldynamichardyhilberttypeinequalitiesontimescaleswithapplications
_version_	1718411386512474112

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

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