Hilbert-type inequalities for time scale nabla calculus

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...

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Bibliographic Details
Published in:	Advances in difference equations Vol. 2020; no. 1; pp. 1 - 21
Main Authors:	Rezk, H. M., AlNemer, Ghada, Abd El-Hamid, H. A., Abdel-Aty, Abdel-Haleem, Nisar, Kottakkaran Sooppy, Zakarya, M.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 04-11-2020 Springer Nature B.V SpringerOpen
Subjects:	Analysis Applications Delta calculus Difference and Functional Equations Functional Analysis Hilbert’s inequality Inequalities Mathematics Mathematics and Statistics Methods Nabla calculus Ordinary Differential Equations Partial Differential Equations Time Time scales Topics in Special Functions and q-Special Functions: Theory 26E70 Hilbert’s inequality Time scales 26D10 Delta calculus Nabla calculus 26D15
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Summary:	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.
ISSN:	1687-1847 1687-1839 1687-1847
DOI:	10.1186/s13662-020-03079-w