A Study on Ratio-Type Dynamic Inequalities on Time Scales
DOI:
https://doi.org/10.31185/bsj.Vol23.Iss48.1917Keywords:
Keywords: Ratio-type inequalities, Chain rule on time scales, Jensen's inequality.Abstract
Abstract This work includes the time scale analogues of some classical integral inequalities of ratio forms with weighted functions to unify the results in the continuous and discrete calculi in a single inequality with general domain called a time scale ???? which is defined as a nonempty closed subset of the real numbers ℝ. The role of proving any inequality on time scales, is to avoid proving this inequality twice (one in the continuous case and the other in the discrete case). Our results, in the continuous case, give the extension of the earlier results established in [12], [7], and [10], while we also can get other different discrete analogues. Additionally, we can obtain other inequalities in the quantum time scale calculus.
References
[1] Agarwal, R. P., O'Regan, D., & Saker, S. H., (2016). Hardy type inequalities on time scales. Springer.
[2] Akın, L., (2021). A new approach for the fractional integral operator in time scales with variable exponent Lebesgue spaces. Fractal and Fractional.
[3] Awwad, E., & Saied, A. I., (2022). Some new multidimensional Hardy-type inequalities with general kernels on time scales. J. Math. Inequal., 393-412
[4] Awwad, E., & Saied, A. I., (2024). Some weighted dynamic inequalities of Hardy type with kernels on time scales nabla calculus. J. Math. Inequal., 457-475.
[5] Bohner, M., & Peterson, A., (2001). Dynamic Equations on Time Scales: An Introduction with Applications. Birkhäuser.
[6] Bennett, G.,&Grosse-Erdmann, K. G., (2006). Weighted Hardy inequalities for decreasing sequences and functions. Mathematische Annalen, 334, 489-531.
[7] Chesneau, C., (2025). On a Weighted ratio-type integral inequality. Journal of Computer Science and
Applied Mathematics, 35-40.
[8] Hardy, G. H., (1928). Notes on some points in the integral calculus (LXIT). Messenger of Math., 57,
12-16.
[9] Hilger, S., (1990). Analysis on measure chains-a unified approach to continuous and discrete calculus. Results in Mathematics, 18(1), 18-56.
[10] Liu, W. J., Ngô, Q. A., & Huy, V. N., (2009). Several interesting integral inequalities. J. Math. Inequal.,
3(2), 201-212.
[11] Lütfi, A., (2021). On innovations of n-dimensional integral-type inequality on time scales. Advances in Continuous and Discrete Models.
[12] Makanin, V., (2014). Solution by V. Makanin, Sankt Petersburg, Russia, Gazeta Matematica, 57-58.
[13] Oguntuase, J. A., & Persson, L. E., (2014). Time scales Hardy-type inequalities via superquadracity. Annals of Functional Analysis, 5(2), 61-73.
[14] Řehák, P., (2005). Hardy inequality on time scales and its application to half-linear dynamic equations. Journal of Inequalities and Applications, 1-13.
[15] Saied, A. I., Jadlovská, I., & Krnić, M., (2025). Some new characterizations of weights for Hardy-type inequalities with kernels on time scales. Mathematica Slovaca, 1063-1076.
[16] Saker, S. H., O'Regan, D., & Agarwal, R., (2014). Generalized Hardy, Copson, Leindler and Bennett inequ
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