Hilbert-type inequalities for time scale nabla calculus

H. M. Rezk; Ghada AlNemer; H. A. Abd El-Hamid; Abdel Haleem Abdel-Aty; Kottakkaran Sooppy Nisar; M. Zakarya

doi:10.1186/s13662-020-03079-w

Hilbert-type inequalities for time scale nabla calculus

H. M. Rezk
, Ghada AlNemer
, H. A. Abd El-Hamid
, Abdel Haleem Abdel-Aty
, Kottakkaran Sooppy Nisar
, M. Zakarya

Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

Original language	English
Article number	619
Journal	Advances in Difference Equations
Volume	2020
Issue number	1
DOIs	https://doi.org/10.1186/s13662-020-03079-w
State	Published - 1 Dec 2020

Keywords

Delta calculus
Hilbert’s inequality
Nabla calculus
Time scales

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10.1186/s13662-020-03079-w

Cite this

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title = "Hilbert-type inequalities for time scale nabla calculus",

abstract = "This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, H{\"o}lder{\textquoteright}s inequality, and Jensen{\textquoteright}s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.",

keywords = "Delta calculus, Hilbert{\textquoteright}s inequality, Nabla calculus, Time scales",

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AU - Rezk, H. M.

AU - AlNemer, Ghada

AU - Abd El-Hamid, H. A.

AU - Abdel-Aty, Abdel Haleem

AU - Nisar, Kottakkaran Sooppy

AU - Zakarya, M.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

AB - This paper deals with the derivation of some new dynamic Hilbert-type inequalities in time scale nabla calculus. In proving the results, the basic idea is to use some algebraic inequalities, Hölder’s inequality, and Jensen’s time scale inequality. This generalization allows us not only to unify all the related results that exist in the literature on an arbitrary time scale, but also to obtain new outcomes that are analytical to the results of the delta time scale calculation.

KW - Delta calculus

KW - Hilbert’s inequality

KW - Nabla calculus

KW - Time scales

UR - https://www.scopus.com/pages/publications/85094967546

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DO - 10.1186/s13662-020-03079-w

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AN - SCOPUS:85094967546

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VL - 2020

JO - Advances in Difference Equations

JF - Advances in Difference Equations

IS - 1

M1 - 619

ER -

Hilbert-type inequalities for time scale nabla calculus

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Keywords

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