Inequalities on Time Scales: A Survey

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Periodic solutions for predator–prey systems with Beddington–DeAngelis functional response on time scales (2008, background): “The proofs of the following lemmas can be found in [4] and [1,13], respectively.”
Lyapunov inequality for linear Hamiltonian systems on time scales (2005, background): “3 (Cauchy–Schwarz inequality [2,5]).”
Diamond- Jensen's Inequality on Time Scales (2007, background): “[3] If g ∈ Crd([a, b], (c, d)) and f ∈ C((c, d), R) is convex, then f ( ∫ b a g(s)∆s b − a )”
Dynamic equations on time scales: a survey (2002, neutral): “…g 2 (t; s) = t s g 1 ((); s)) = t s (() − s)) = t s (() + )) − t s − t s s = t s ( 2 ) + s t − s(t − s) = s t + t 2 − s 2 − s(t − s) = s t ( − t)) = s t h 1 (; t)) = h 2 (s; t): One of the two versions of Taylor's formula (the other obtained by using (2.5)) reads as follows, see [2]: Theorem 2.3.”
Dynamic Equations on Time Scales: An Introduction with Applications (2001, background): “Find the functions hk(·, 0), for k = 0, 1, 2, 3 if T := [0, 1] ∪ [3, 4].”
An Extension of Jensen's Inequality on Time Scales (2006, background): “The Jensen inequality has been extended to time scales by Agarwal, Bohner, and Peterson as follows (see [1,3]): Theorem 1.”
Impulsive differential equations and inclusions (2006, neutral): “14 (see [4]).”