We first establish q-non uniform difference versions of the integral inequalities of Hölder, Cauchy-Schwarz, and Minkowski of classical mathematical analysis and then integral inequalities of Grönwall and Bernoulli based on the Lagrange method of linear q-non uniform difference equations of first order. Finally, we prove the Lyapunov inequality for the solutions of the q-non uniform Sturm-Liouville equation.
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