The aim of present paper is to obtain Shannon type inequalities using the extended version of Jensen's inequality in time scales settings. The concept of differential entropy of a continuous random variable on time scales is introduced, and its bounds for some particular distributions are also estimated.
In this paper, we present some inequalities for Csiszár f-divergence between two probability measures on time scale. These results extend some known results in the literature and offer new results in h-discrete calculus and quantum calculus. We also present several inequalities for divergence measures.
The main purpose of the presented paper is to obtain some time scale inequalities for different divergences and distances by using weighted time scales Jensen’s inequality. These results offer new inequalities in h-discrete calculus and quantum calculus and extend some known results in the literature. The lower bounds of some divergence measures are also presented. Moreover, the obtained discrete results are given in the light of the Zipf–Mandelbrot law and the Zipf law.
Taylor’s polynomial and Green’s function are used to obtain new generalizations of an inequality for higher order convex functions containing Csiszár divergence on time scales. Various new inequalities for some divergence measures in quantum calculus and h-discrete calculus are also established.
The aim of the present paper is to obtain new generalizations of an inequality for n-convex functions involving Csiszár divergence on time scales using the Green function along with Fink’s identity. Some new results in h-discrete calculus and quantum calculus are also presented. Moreover, inequalities for some divergence measures are also deduced.
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