Cauchy's equation on Δ+: Further results
Copyright policy )Cauchy's equation on Δ+: Further results
In continuation of his paper [ibid. 41, No. 2/3, 192-211 (1991; Zbl 0733.39012)] the author deals under weak conditions with the functional equation \(\varphi(\tau_{T,L}(F,G))=\tau_{T,L}(\varphi(F),\varphi(G))\) for all probability distributions \(F,G\) of nonnegative random variables. Here \(T(x,y)=g^{(-1)}(g(x)+g(y))\), \(L(u,v)=f^{(-1)}(f(u)+f(v))\). \((f(0)=0,f:\mathbb{R}_ +\to\mathbb{R}_ +\) is continuous, strictly increasing and \(f^{(-1)}\) is its pseudo-inverse), and \(\tau_{T,L}(F,G)(x)=\sup_{L(u,v)=x}T(F(u),G(v))\).
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Functional equations for real functions, Characteristic functions; other transforms, lattices, Metric spaces, metrizability, Cauchy equation, continuous, archimedean \(t\)-norms, Functional equations for functions with more general domains and/or ranges, probability distributions, associative functions, pseudo-inverse
Functional equations for real functions, Characteristic functions; other transforms, lattices, Metric spaces, metrizability, Cauchy equation, continuous, archimedean \(t\)-norms, Functional equations for functions with more general domains and/or ranges, probability distributions, associative functions, pseudo-inverse
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