Solution of a functional equation arising from utility that is both separable and additive
نویسندگان
چکیده
منابع مشابه
Solution of a Functional Equation Arising from Utility That Is Both Separable and Additive
The problem of determining all utility measures over binary gambles that are both separable and additive leads to the functional equation f(v) = f(vw) + f [vQ(w)], v, vQ(w) ∈ [0, k), w ∈ [0, 1] . The following conditions are more or less natural to the problem: f strictly increasing, Q strictly decreasing; both map their domains onto intervals (f onto a [0, K), Q onto [0, 1]); thus both are con...
متن کاملA Functional Equation Arising from Ranked Additive and Separable Utility
All strictly monotonic solutions of a general functional equation are determined. In a particular case, which plays an essential role in the axiomatization of rank-dependent expected utility, all nonnegative solutions are obtained without any regularity conditions. An unexpected possibility of reduction to convexity makes the present proof possible.
متن کاملSolution of a Functional Equation Arising in an Axiomatization of the Utility of Binary Gambles
For a new axiomatization, with fewer and weaker assumptions, of binary rank-dependent expected utility of gambles the solution of the functional equation (z/p)γ−1[zγ(p)] = φ−1[φ(z)ψ(p)] (z, p ∈]0, 1[) is needed under some monotonicity and surjectivity conditions. We furnish the general such solution and also the solutions under weaker suppositions. In the course of the solution we also determin...
متن کاملStability of additive functional equation on discrete quantum semigroups
We construct a noncommutative analog of additive functional equations on discrete quantum semigroups and show that this noncommutative functional equation has Hyers-Ulam stability on amenable discrete quantum semigroups. The discrete quantum semigroups that we consider in this paper are in the sense of van Daele, and the amenability is in the sense of Bèdos-Murphy-Tuset. Our main result genera...
متن کاملThe Continued Utility and Viability of Dakin’s Solution in Both High- and Low-resource Settings
Healthcare is expensive and often inaccessible to many. As a result, surgeons must consider simple, less expensiveinterventions when possible. For wound care, an older but quite effective cleaning agent is Dakin’s solution (0.5%sodium hypochlorite), an easily made mixture of 100 milliliters (ml) bleach with 8 teaspoons (tsp) baking soda into agallon of clean water or 25 ml ble...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1999
ISSN: 0002-9939,1088-6826
DOI: 10.1090/s0002-9939-99-04863-7