Turkish Journal of Science
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Journal

Turkish Journal of Science


Volume
& Issue

Volume 9, Issue 1


Published
on

April 8, 2024


Pages

54-67


DOI

Article

Dynamic Hardy-Littlewood Type Inequalities via Time Scales Involving Nabla Integrals

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Authors

Ammara NOSHEEN Affiliation:
Department of Mathematics, University of Sargodha, Sargodha 40100, Punjab, Pakistan
, Khuram Ali KHAN Affiliation:
Department of Mathematics, University of Sargodha, Sargodha 40100, Punjab, Pakistan
and Muhammad Rizwan SHABBIR Affiliation:
Department of Mathematics, University of Sargodha, Sargodha 40100, Punjab, Pakistan


Abstract

Hardy-Littlewood inequalities via nabla time scales calculus are studied in this paper. The results are proved by using time scales analogues of chain rule, Holder’s inequality, some algebraic inequalities, and integration by parts. Particular cases include some discrete novel Hardy-Littlewood inequalities by fixing time scales. Moreover, special cases also include some existing integral and discrete Hardy-Littlewood inequalities in literature.


Keywords

time scales calculus, Hardy-Littlewood inequalities, integral inequalities, discrete inequalities.


Citation

Nosheen, A., Khan, K. A., & Shabbir, M. R. (2024). Dynamic hardy-littlewood type inequalities via time scales involving nabla integrals. Turkish Journal of Science, 9(1), 54–67. https://doi.org/10.66833/TJOS-2024-0006
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