## On a generalization of a functional equation associated with the distance between the probability distributions.(English)Zbl 0860.39032

From the authors’ abstract: The functional equation $f(pr,qs) + f(ps,qr) = g(p, q) f(r,s) + g(r,s)f(p,q)\qquad (p,q,r,s \in]0,1])$ where $$f$$ and $$g$$ are complex-valued functions defined on $$]0,1]$$, is solved without any regularity assumptions. This functional equation is a generalization of a functional equation which was instrumental in the characterization of the symmetric divergence of degree $$\alpha$$ studied by J. K. Chung, Pl. Kannappan, C. T. Ng and P. K. Sahoo [J. Math. Anal. Appl. 138, No. 1, 280-292 (1989; Zbl 0669.60025)].

### MSC:

 39B32 Functional equations for complex functions 60E05 Probability distributions: general theory 94A17 Measures of information, entropy

Zbl 0669.60025