Search results for "Bornology"

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Contribution to variational analysis : stability of tangent and normal cones and convexity of Chebyshev sets

2014

The aim of this thesis is to study the following three problems: 1) We are concerned with the behavior of normal cones and subdifferentials with respect to two types of convergence of sets and functions: Mosco and Attouch-Wets convergences. Our analysis is devoted to proximal, Fréchet, and Mordukhovich limiting normal cones and subdifferentials. The results obtained can be seen as extensions of Attouch theorem to the context of non-convex functions on locally uniformly convex Banach space. 2) For a given bornology β on a Banach space X we are interested in the validity of the following "lim inf" formula (…).Here Tβ(C; x) and Tc(C; x) denote the β-tangent cone and the Clarke tangent cone to …

Contingent coneCône tangent de BouligandSuite minimisanteFonctions sous-régulières cône normal (tangent) de ClarkeClarke tangent (normal) coneMetric projection[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]Chebyshev setMosco (Attouch-Wets) convergenceAsplund spaceCône normal proximalProjection metriqueEnsemble de ChebyshevConvergence au sens de Mosco (d'Attouch-Wets)Subsmooth sets (functions)BornologyBornologieMinimizing sequenceProximal normal coneFréchet (Mordukhovich limiting) subdifferentialEspace d'AsplundTrustworthinessSous-différentiel de Fréchet (de Mordukhovich)Ensembles sous-réguliers
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MR2481817 (2010e:46040): Haluška, Ján; Hutník, Ondrej On vector integral inequalities. Mediterr. J. Math. 6 (2009), no. 1, 105–124. (Reviewer: Luisa …

2009

I. Dobrakov in his papers [Czechoslovak Math. J. 40(115) (1990), no. 1, 8--24; MR1032359 (90k:46097); Czechoslovak Math. J. 40(115) (1990), no. 3, 424--440; MR1065022 (91g:46052)] developed a theory for integrating vector-valued functions with respect to operator-valued measures: Let X and Y be two Banach spaces, Δ be a δ-ring of subsets of a nonempty set T, L(X,Y) be the space of all continuous operators L:X→Y, and m:Δ→L(X,Y) be an operator-valued measure σ-additive in the strong operator topology of L(X,Y). A measurable function f:T→X is said to be integrable in the sense of Dobrakov if there exists a sequence of simple functions fn:T→X, n∈N, converging m-a.e. to f and the integrals ∫.fnd…

bornologyvector functionDobrakov integralintegral inequalityInductive limit of Banach space
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