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Monotonic Solutions of a Functional Equation Arising from Simultaneous Utility Representations

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Abstract

The functional equation ƒ(h(x)) − ƒ(h(y)) + ƒ(y) = ƒ(h(x − y) + y) was solved by Aczél, Luce and Marley on the assumption that the functions are different iable. They posed the question of its strictly monotonic continuous solutions. The problem is solved using a uniqueness theorem. The continuity assumption on the functions is removed and the equation is also solved on a restricted domain.

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  1. Department of Pure Mathematics, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1

    Che Tat Ng

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  1. Che Tat Ng
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Correspondence to Che Tat Ng.

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Ng, C.T. Monotonic Solutions of a Functional Equation Arising from Simultaneous Utility Representations. Results. Math. 44, 340–361 (2003). https://doi.org/10.1007/BF03322990

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  • DOI: https://doi.org/10.1007/BF03322990

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