Abstract:We prove some weighted inequalities for delta derivatives acting on products and compositions of functions on time scales and apply them to obtain generalized dynamic Opial-type inequalities. We also employ these inequalities to establish some new dynamic Lyapunov-type inequalities, which are essential in studying disfocality, disconjugacy, lower bounds of eigenvalues, and distance between generalized zeros for half-linear dynamic equations. In particular, we solve an open problem posed by Saker in [Math. Comp… Show more
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