On Shannon and Zipf–Mandelbrot entropies and related results

Abstract

Abstract In this paper, we present some interesting results related to the bounds of the Shannon and the Zipf–Mandelbrot entropies. Further, we define linear functionals and present their properties. We also construct new family of exponentially convex functions and Cauchy-type means.

Keywords

• Shannon entropy
• Zipf–Mandelbrot entropy
• Non-increasing sequence in weighted mean
• Wright-convex function
• Cauchy means
• n-exponential convexity and logarithmic convexity