Abstract
The functional equationg(u, x)+g(v, y)=g(u, y)+g(v, x) for allu, v, x, y>0 withu+v=x+y is initiated by F. A. Cowell and A. F. Shorrocks in their research on the aggregation of inequality indices. We solve the equation by extension theorems.
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Dedicated to Professor Janos Aczél on his 60th birthday
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Ng, C.T. On a functional equation related to income inequality measures. Aeq. Math. 28, 161–169 (1985). https://doi.org/10.1007/BF02189408
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DOI: https://doi.org/10.1007/BF02189408