Article
Dynamic Hardy-Littlewood Type Inequalities via Time Scales Involving Nabla Integrals
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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
A. Nosheen, K. A. Khan and M. R. Shabbir, “Dynamic hardy-littlewood type inequalities via time scales involving nabla integrals,” Turkish Journal of Science, vol. 9, no. 1, pp. 54–67, 2024, doi: 10.66833/TJOS-2024-0006.
Nosheen A, Khan KA, Shabbir MR. Dynamic hardy-littlewood type inequalities via time scales involving nabla integrals. Turkish Journal of Science. 2024;9(1):54–67. doi:10.66833/TJOS-2024-0006.
Nosheen, A., Khan, K. A. and Shabbir, M. R. (2024), ‘Dynamic hardy-littlewood type inequalities via time scales involving nabla integrals’, Turkish Journal of Science, 9(1), pp. 54–67. Available at: https://doi.org/10.66833/TJOS-2024-0006.
Nosheen, Ammara, et al. “Dynamic Hardy-littlewood Type Inequalities via Time Scales Involving Nabla Integrals.” Turkish Journal of Science, vol. 9, no. 1, 2024, pp. 54–67. https://doi.org/10.66833/TJOS-2024-0006.
Nosheen, Ammara, Khuram Ali Khan, and Muhammad Rizwan Shabbir. “Dynamic Hardy-littlewood Type Inequalities via Time Scales Involving Nabla Integrals.” Turkish Journal of Science 9, no. 1 (2024): 54–67. https://doi.org/10.66833/TJOS-2024-0006.
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- DOI: 10.66833/tjos-2024-0006
- Type: article
- Source: Turkish Journal of Science
- Published: 2024-04-30
- OpenAlex ID: W7171950058
Published by: Engineering Journals


