Abstract
The functional equationf(x,y)+g(x)h(y)F(u/1−x,ν/1−y)=f(u,ν)+g(u)h(ν)F(x/1−u,y/1−ν) ... (1) forx, y, u, ν ∈ [0, 1) andx+u,y+ν ∈ [0,1) whereg andh satisfy the functional equationφ (x+y−xy)=φ(x)φ(y)... (2) has been solved for some non-constant solution of (2) in [0, 1] withφ (0)=1,φ(1)=0 and the solution is used in characterising some measures of information.
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Patni, G.C., Jain, K.C. Generalized functional equation and its applications in information theory. Proc. Indian Acad. Sci. 86, 353–364 (1977). https://doi.org/10.1007/BF03046850
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DOI: https://doi.org/10.1007/BF03046850