Weighted Ostrowski, Ostrowski-Grüss and Ostrowski-Čebyšev type inequalities on time scales (Q2915420)

Recently several authors have extended various classical inequalities to inequalities on time scales, an important concept due to Hilger that enables discrete and continuous results to be proved simultaneously, see in particular \textit{R. Agarwal, M. Bohner and A. Peterson} [Math. Inequal. Appl. 4, 535--557 (2001; Zbl 1021.34005)], \textit{M. Bohner and A. Peterson} [Dynamic equations on time scales. An introduction with applications, Basel: Birkhäuser (2001; Zbl 0978.39001)] a list of papers is included in the bibliography of the present paper. This paper concentrates on weighted versions of various inequalities considered earlier in papers by Liu and others; see \textit{W. Liu, N. Q. Ahn and W. Chen} [J. Inequal. Appl. 2008, Article ID 597241 (2008; Zbl 1175.26044)], \textit{W. Liu, N. Q. Ahn and W. Chen} [Dyn. Syst. Appl. 19, 189--198 (2010; Zbl 1200.26042)], \textit{M. F. Betta, F. Brock, A. Mercaldo and M. R. Posteraro} [Math. Nachr. 281, 466--498 (2008; Zbl 1144.26030)]. The theorems proved are too complicated to be given here but are significant extensions of the known results. Proofs are not difficult once the background material has been assembled. and the correct results identified.