Levinson’s Functional in Time Scale Settings

Author:

Barić Josipa1

Affiliation:

1. Faculty of Electrical Engineering Mechanical Engineering and Naval Architecture, University of Split, 21000 Split, Croatia

Abstract

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

Publisher

MDPI AG

Subject

Geometry and Topology,Logic,Mathematical Physics,Algebra and Number Theory,Analysis

Reference17 articles.

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2. Integral inequalities of Levinson’s type in time scale settings;Math. Inequalities Appl.,2019

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4. Sur une inealite de N. Levinson;Popoviciu;Mathematica,1964

5. An inequality of N. Levinson;Bullen;Publ. Elektrotehn. Fak. Ser. Mat. Fiz.,1973

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