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This paper is devoted to finding the general solutions of the functionalequation  $\sumin \sumjm h(p_iq_j)=\sumin h(p_i)+\sumjm k_j(q_j)+\lambda\suminh(p_i)\sumjm k_j(q_j)$  valid for all complete probability distributions $(p_1,\ldots,p_n)$,$(q_1,\ldots,q_m)$, $0\le p_i\le 1$, $0\le q_j\le 1$, $i=1,\ldots,n$;$j=1,\ldots,m$, $\sumin p_i=1$, $\sumjm q_j=1$; $n\ge 3$, $m\ge 3$ fixedintegers; $\lambda\in\RR$, $\lambda\neq 0$ and the mappings $h:I\to\RR$,$k_j:I\to\RR$, $j=1,\ldots,m$; $I=[0,1]$, $\RR$ denoting the set of all realnumbers. A special case of the above functional equation was treated earlier byL. Losonczi and Gy. Maksa.

A sum form functional equation on a closed domain and its role in information theory