Estimation of entropies on time scales by Lidstone's interpolation using Csiszár-type functional

Abstract

The inequality containing Csiszár divergence on time scales is generalized for $2n$-convex functions by using Lidstone interpolating polnomial. As an application, new entropic bounds on time scales are also computed. Several inequalities in quantum calculus and $h$-discrete calculus are also established. The relationship between Shannon entropy, Kullback-Leibler divergence and Jeffreys distance with Zipf-Mandelbrot entropy are also established.

Keywords

• time scales calculus
• convex function
• Lidstone’s interpolating polynomial
• information theory

Supporting Institution

The research of 5th author (Josip Pecaric) is supported by the Ministry of Education and Science of the Russian Federation

Project Number

Agreement number 02.a03.21.0008).

Thanks

The authors would like to express their sincere thanks to the anonymous reviewers for their helpful comments and suggestions.

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