Inequalities on Time Scales

Abstract

Here first we collect and develop necessary background on time scales required for this chapter. Then we give time scales integral inequalities of types: Poincaré, Sobolev, Opial, Ostrowski and Hilbert-Pachpatte. We present also the generalized analogs of all these inequalities involving high order delta derivatives of functions on time scales. We finish with many applications: all these inequalities on the specific time scales ℝ, ℤ and $q^{\overline{\mathbb{Z}}}$, q > 1. This chapter relies on [57].