Labora tory experiments have repeatedly shown that decision makers do not satisfy the expected utility hypothesis. The evidence did not discourage the use of expected utility, partly because it was a useful paradigm and partly due to the lack of convenient alternatives. Furthermore, it was not clear that the results obtained by expected utility theory do not hold for more general models. Indeed...

New elements of calculus on a complete real closed non-Archimedean field extension F of the real numbers R will be presented. It is known that the total disconnectedness of F in the topology induced by the order makes the usual (topological) notions of continuity and differentiability too weak to extend real calculus results to F . In this paper, we introduce new stronger concepts of continuity...

We study Lipschitz differentiability spaces, a class of metric measure spaces introduced by Cheeger in [8]. We show that if an Ahlfors regular Lipschitz differentiability space has charts of maximal dimension, then, at almost every point, all its tangents are uniformly rectifiable. In particular, at almost every point, such a space admits a tangent that is isometric to a finite-dimensional Bana...

Let Kn be the Lorentz/second-order cone in R. For any function f from R to R, one can define a corresponding function f soc(x) on R by applying f to the spectral values of the spectral decomposition of x ∈ R with respect to Kn. We show that this vector-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiabi...

adomian decomposition method has been applied to solve many functional equations so far. in this article, we have used this method to solve the fuzzy differential equation under generalized differentiability. we interpret a fuzzy differential equation by using the strongly generalized differentiability. also one concrete application for ordinary fuzzy differential equation with fuzzy input data...

This article studies continuity and directional differentiability properties of optimal value functions, in particular at boundary points of their domain. We extend and complement standard continuity results from [12] for abstract feasible set mappings under complete convexity as well as standard differentiability results from [13] for feasible set mappings in functional form under the Slater c...

We consider optimal control problems governed by nonlinear hyperbolic conservation laws at junctions and analyze in particular the Fréchet-differentiability of the reduced objective functional. This is done by showing that the control-to-state mapping of the considered problems satisfies a generalized notion of differentiability. We consider both, the case where the controls are the initial and...

For any function f from R to R, one can define a corresponding function on the space of n × n (block-diagonal) real symmetric matrices by applying f to the eigenvalues of the spectral decomposition. We show that this matrix-valued function inherits from f the properties of continuity, (local) Lipschitz continuity, directional differentiability, Fréchet differentiability, continuous differentiab...