On the sum form functional equation related to diversity index

Abstract

The focal point of this article is to study a functional equation of sum form involving four unknown mappings. We primarily concentrate on exploring all possible solutions of the equation. An attempt is made to delve into the intricacies of obtaining these solutions without assuming any regularity condition on the mappings. Our study further aims to examine the stability of these general solutions, thus shedding light on the behaviour of sum form functional equations under perturbations. The article concludes by reflecting upon the relevance of the general solutions in information theory and diversity index.

Keywords

• logarithmic mapping
• multiplicative mapping
• sum form functional equation
• discrete random variable
• mean of a discrete random variable
• entropies
• 39b52
• 39b82