Agarwal, Ravi P.; Otero-Espinar, Victoria; Perera, Kanishka; Vivero, Dolores R. Wirtinger’s inequalities on time scales. (English) Zbl 1148.26020 Can. Math. Bull. 51, No. 2, 161-171 (2008). Summary: This paper is devoted to the study of Wirtinger-type inequalities for the Lebesgue \(\Delta\)-integral on an arbitrary time scale \(T\). We prove a general inequality for a class of absolutely continuous functions on closed subintervals of an adequate subset of \(T\). By using this expression and by assuming that \(T\) is bounded, we deduce that a general inequality is valid for every absolutely continuous function on \(T\) such that its Delta-derivative belongs to \(L^2_{\Delta} ([a,b) \cap T)\) and at most it vanishes on the boundary of \(T\). Cited in 8 Documents MSC: 26D15 Inequalities for sums, series and integrals PDFBibTeX XMLCite \textit{R. P. Agarwal} et al., Can. Math. Bull. 51, No. 2, 161--171 (2008; Zbl 1148.26020) Full Text: DOI