The general solution of a functional equation related to the characterizations of bivariate distributions

Decomposition of functional equations with applications

“…In paper [13] was investigated the case when X = F + where F = F(+, •) is an ordered field (the operation • is commutative) the T + is the set of positive elements of the F, x • y := x y+1 for all x, y ∈ F + , Y = Y (+) is a uniquely two-divisible Abelian group. In this settings the general solution of Equation (2.6) is…”

“…In this settings the general solution of Equation (2.6) is (Concerning the additive and logarithmic functions see [1], and [17]). This result could perhaps be improved writing simply ordered field instead of Archimedean ordered field, that is, The above two problems have probability background see [18], [2], [13], and [11]. Two pairs of new equations can be derived from the above two equations, the Pexider versions of the second of these equations (which contain the unknown gamma function) characterize the logarithmic functions see [12].…”