Akin-Bohner, Elvan; Bohner, Martin; Akin, Faysal Pachpatte inequalities on time scales. (English) Zbl 1086.34014 JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 6, 23 p. (2005). The authors prove a variety of inequalities within the context of the calculus on time scales. Here, the involved functions are assumed to be defined on arbitrary closed subsets \({\mathbb T}\) of the reals and the crucial notion is the so-called delta derivative generalizing the usual derivative (for \({\mathbb T}={\mathbb R}\)) and the forward difference operator (for \({\mathbb T}={\mathbb Z}\)).More precisely, comparison principles are used to derive time scale versions of certain inequalities, which in the special cases \({\mathbb T}={\mathbb R}\) or \({\mathbb T}={\mathbb Z}\) date back to Gronwall, Gamidov (or in the discrete case, to Pachpatte), Gollwitzer, Norbury and Stuart (Volterra-type inequalities), Green (in the discrete case, to Pachpatte) and Ma. These results are supplemented by several corollaries. Finally, also inequalities involving first- and second-order delta derivatives are addressed (originally due to Pachpatte). Reviewer: Christian Pötzsche (Minneapolis) Cited in 46 Documents MSC: 34A40 Differential inequalities involving functions of a single real variable 39A10 Additive difference equations 39A13 Difference equations, scaling (\(q\)-differences) Keywords:time scales; Pachpatte inequalities; dynamic inequalities PDF BibTeX XML Cite \textit{E. Akin-Bohner} et al., JIPAM, J. Inequal. Pure Appl. Math. 6, No. 1, Paper No. 6, 23 p. (2005; Zbl 1086.34014) Full Text: EuDML