Extensions of certain integral inequalities on time scales. (English) Zbl 1168.26316
Summary: We establish Hölder’s inequality, Minkowski’s inequality and Jensen’s inequality on time scales via the nabla integral and diamond-\(\alpha \) dynamic integral, which is defined as a linear combination of the delta and nabla integrals.
Keywords:
delta and nabla integrals; diamond-\(\alpha \) integral; Hölder’s inequality; Minkowski’s inequality; Jensen’s inequalityReferences:
| [1] | Atici, F. M.; Guseinov, G. Sh., On Green’s functions and positive solutions for boundary value problems on time scales, J. Comput. Appl. Math., 141, 75-99 (2002) · Zbl 1007.34025 |
| [2] | Bohner, M.; Peterson, A., Dynamic equations on time scales, (An Introduction with Appl. (2001), Birkhauser: Birkhauser Boston) · Zbl 1021.34005 |
| [3] | Bohner, M.; Peterson, A., Advances in Dynamic Equations on Time Scales (2003), Birkhauser: Birkhauser Boston, MA · Zbl 1025.34001 |
| [4] | S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Würzburg, 1988; S. Hilger, Ein Maßkettenkalkül mit Anwendung auf Zentrmsmannigfaltingkeiten, Ph.D. Thesis, Univarsi. Würzburg, 1988 · Zbl 0695.34001 |
| [5] | Maligranda, L., Why Hölder’s inequality should be called Roger’s inequality, Math. Inequal. Appl., 1, 69-83 (1998) · Zbl 0889.26001 |
| [6] | Sheng, Q.; Fadag, M.; Henderson, J.; Davis, J. M., An exploration of combined dynamic derivatives on time scales and their applications, Nonlinear Anal. RWA, 7, 395-413 (2006) · Zbl 1114.26004 |
| [7] | Wong, F.-H.; Yeh, C.-C.; Yu, S.-L.; Hong, C.-H., Young’s inequality and related results on time scales, Appl. Math. Lett., 18, 983-988 (2005) · Zbl 1080.26025 |
| [8] | Wong, F.-H.; Yeh, C.-C.; Lian, W.-C., An extension of Jensen’s inequality on time scales, Adv. Dynam. Syst. Appl., 1, 1, 113-120 (2006) · Zbl 1123.26021 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
