On a functional equation on groups arising from the characterization of stochastic distance measures

This work aims to determine all functions f,g,h,k:G→C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${f, g, h, k : G \to \mathbb{C}}$$\end{document} that satisfy the functional equation f(pr, qs) + g(ps, qr) =  h(p,q) +  k(r,s) for all p, q, r, s ∈G, where G is a group and C\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb{C}}$$\end{document} is the field of complex numbers.