Set valued functions in Fréchet spaces: Continuity, Hukuhara differentiability and applications to set differential equations

Set integral equations in metric spaces

“…Our results generalize and extend the results given in [2]. For other similar results see [3], [5] and [4].…”

Set Differential Equations in Fréchet Spaces

“…A way out, at least partially, of these problems has been proposed in [2]. Generalizations of all the above notions have been developed in order to fit in the structure of a wide category of locally convex topological vector spaces: The Fréchet (i.e.…”

“…In an earlier paper [2], we proposed the generalizations of the above notions to a wide class of locally convex topological vector spaces: the Fréchet spaces. Making ample use of the fact that every Fréchet space F can be viewed also as a projective limit of Banach spaces, we established on K c (F) a separable and complete topological structure.…”

Infinitesimal calculus in metric spaces

“…Among the fields which required such generalizations are the following topics: differential equations ( [31]), duality ([50], [54]...), evolution of domains ( [5], [6], [57], [58]), geometry ([34]- [36]), image reconstruction ( [29], [47], [49]), mechanics ([42], [51]), morphogenesis ( [5]), nonlinear analysis and optimization ( [2], [18], [25], [22]), shape optimization ( [1], [5], [11], [13], [24], [37], [27], [28], [62]), stochastic problems ( [45], [56]), viability and invariance ( [26], [59]). Several models exist: Cartesian squares, metric measure spaces ( [2], [21], [38], [39], [40]...), mutational spaces ( [5], [6], [26]- [28]...) and their variants ( [19]...) with various purposes.…”