Nabla time scales inequalities (Q2429743)

Summary: Here first we collect and develop necessary background on nabla time scales required for this paper. Then we present nabla time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert-Pachpatte. We give also the generalised analogues of all these nabla inequalities involving high order nabla derivatives of functions on time sclaes. We finish with lots of applications: all these nabla inequalities on the specific time scales \(\mathbb R\), \(\mathbb Z\) and \(q^{\overline{\mathbb Z}}\), \(q>1\). In most of these nabla inequalities the nabla differentiability order is any \(n\in\mathbb N\), as opposed to delta time scales approach where \(n\) is always odd.