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Symmetry
Volume 14
Issue 4
10.3390/sym14040802
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Article

Hardy–Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus

by
Ammara Nosheen
1,†,
Huma Akbar
2,
Maroof Ahmad Sultan
3,
Jae Dong Chung
4 and
Nehad Ali Shah
4,*,†
1
Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan
2
Department of Mathematics and Statistics, The University of Lahore, Sargodha Campus, Sargodha 40100, Pakistan
3
Nusrat Jahan College Chenab Nagar, Chiniot 35400, Pakistan
4
Department of Mechanical Engineering, Sejong University, Seoul 05006, Korea
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work and are co-first authors.
Symmetry 2022, 14(4), 802; https://doi.org/10.3390/sym14040802
Submission received: 9 March 2022 / Revised: 28 March 2022 / Accepted: 5 April 2022 / Published: 12 April 2022
(This article belongs to the Special Issue Mathematical Inequalities, Special Functions and Symmetry)
Versions Notes

Abstract

In this paper, Hardy–Leindler, Hardy–Yang and Hwang type inequalities are extended on time scales calculus. These extensions are depending upon use of symmetric multiple delta integrals. The target is achieved by utilizing some inequalities in literature along with mathematical induction principle and Fubini’s theorem on time scales. The obtained inequalities are discussed in discrete, continuous and quantum calculus in search of applications. Particular cases of proved results include Hardy, Copson, Hardy–Littlewood, Levinson and Bennett-type inequalities for symmetric sums.
Keywords: Hardy-type inequalities; Leindler-type inequalities; Yang- and Hwang-type inequalities; time scales calculus Hardy-type inequalities; Leindler-type inequalities; Yang- and Hwang-type inequalities; time scales calculus

Share and Cite

MDPI and ACS Style

Nosheen, A.; Akbar, H.; Sultan, M.A.; Chung, J.D.; Shah, N.A. Hardy–Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus. Symmetry 2022, 14, 802. https://doi.org/10.3390/sym14040802

AMA Style

Nosheen A, Akbar H, Sultan MA, Chung JD, Shah NA. Hardy–Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus. Symmetry. 2022; 14(4):802. https://doi.org/10.3390/sym14040802

Chicago/Turabian Style

Nosheen, Ammara, Huma Akbar, Maroof Ahmad Sultan, Jae Dong Chung, and Nehad Ali Shah. 2022. "Hardy–Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus" Symmetry 14, no. 4: 802. https://doi.org/10.3390/sym14040802

APA Style

Nosheen, A., Akbar, H., Sultan, M. A., Chung, J. D., & Shah, N. A. (2022). Hardy–Leindler, Yang and Hwang Inequalities for Functions of Several Variables via Time Scale Calculus. Symmetry, 14(4), 802. https://doi.org/10.3390/sym14040802

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