On Zipf–Mandelbrot entropy

Zipf–Mandelbrot entropy has many applications in many applied sciences, for example, in information theory, ecology and economics, etc. The main purpose of this paper is to associate results for convex functions with Zipf–Mandelbrot entropy. First of all, we present some inequalities for convex functions and their applications for Csiszar divergence. Then we use two classes of convex functions and apply inequalities for convex functions and establish several results for Zipf–Mandelbrot entropy. Related results for Zipf–Mandelbrot entropies corresponding to different parameters have been proved. © 2018 Elsevier B.V.