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

Riedel, T.; Sahoo, P. K.

Publ. Math. Debr. 46, No. 1-2, 125-135 (1995).

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)].

Reviewer: Pl.Kannappan (Waterloo/Ontario)

MSC:

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

Keywords:

functional equation; probability distributions; symmetric divergence

Citations:

Zbl 0669.60025