Generalizations of cyclic refinements of Jensen's inequality by Lidstone's polynomial with applications in information theory

摘要

Jensen’s inequality plays pivotal role in attaining divergence between probability distributions.Shannon, Relative and Zipf-Mandelbrot entropies have ample applications in manyapplied sciences, especially in information theory, biology, economics, etc. In the present paper,we have obtained new generalizations of cyclic refinements of Jensen’s inequality using differentnew Green functions by employing Lidstone’s polynomial. As an application of our obtainedresults we have given new entropic bounds. Also, we have established the connections betweenShannon and Relative entropy with Zipf-Mandelbrot entropy.