Estimation of different entropies via Lidstone polynomial using Jensen-type functionals

In this work, some new functional of Jensen-type inequalities are constructed using Shannon entropy, f-divergence, and Rényi divergence, and some estimates are obtained for these new functionals. Also using the Zipf–Mandelbrot law and hybrid Zipf–Mandelbrot law, we investigate some bounds for these new functionals. Furthermore, we generalize these new functionals for m-convex function using Lidstone polynomial.