Levinson’s Functional in Time Scale Settings

We introduce the Levinson functional on time scales using integral inequality of Levinson’s type in terms Δ-integral for convex (concave) functions scale sets and investigate its properties such as superadditivity monotonicity. The obtained are used to derive bounds given those results provide a refinement converse known scales. Further, we define new types functionals weighted generalized power means scales, prove their which can be employed future works obtain refinements converses inequalities