Set-Valued Analysis

By Z. Denkowski, Stanislaw Migórski, N. Papageorgiou. 2021

2,404 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/c153e1d32c4f43ce92740c28b21e6fb41dbbca16

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Citations in the corpus

Finite time stability and stabilization of a class of continuous systems (2006, background): “The theorem 17 of Mickael given in [20] will help us to show our main result on finite time stabilization.”
Signal Recovery by Proximal Forward-Backward Splitting (2005, background): “Indeed, since ϕ ∈ Γ 0 ( X ), ∂ϕ is maximal monotone [76, Theorem 3.1.11] and its graph is therefore sequentially weakly-strongly closed in X × X [4, Proposition 3.5.6.2].”
Mayer control problem with probabilistic uncertainty on initial positions (2018, neutral): “By Filippov’s Implicit Function Theorem (see e.g. Theorem 8.2.10 in [5]), there exists a Borel map y 7→ u εy ∈ B( 0 , 1 ) satisfying p µ (x),v i dµ(x) by Remark 4.2, we have recalling the optimality of γ .”
Global exponential convergence in a delayed almost periodic Nicholson's blowflies model with discontinuous harvesting (2018, neutral): “In view of (5), (7), (13), and (18), direct calculation produces 0 ≥ x(t2) = −δ(t2)x(t2) + p(t2) a(t2)22 − τ(t2))e −a(t2)x(t2−τ(t2)) − q(t2) γ(t2) x(t2) x(t2) ≥ −δ(t2)κ1 + p(t2) a(t2)1 −κ1 − q(t2)Nκ1 = κ1 [ −δ(t2) + p(t2) a(t2) e−κ1 − q(t2)N ]”
Convex Functions: Constructions, Characterizations and Counterexamples (2010, methodology): “In addition to addressing issues raised by the previous example, limits of sets, or epigraphical convergence as applied to epigraphs of functions, is an important tool in the study of multifunctions as seen in works such as [22].”
A Bellman approach for two-domains optimal control problems in R N (2011, background): “Since the set-valued map B is upper semi-continuous with convex compact images, thanks to [1], Theorem 10.”
Existence results for boundary-value problems with nonlinear fractional differential inclusions and integral conditions. (2010, background): “For more details on multivalued maps see the books of Aubin and Cellina [3], Aubin and Frankowska [4], Deimling [18], and Hu and Papageorgiou [35].”
Differential inclusions in Wasserstein spaces: The Cauchy-Lipschitz framework (2020, methodology): “We refer the reader to [13] for most of the results which are stated below, as well as for a general treatment of this topic.”
Generalized Directional Gradients, Backward Stochastic Differential Equations and Mild Solutions of Semilinear Parabolic Equations (2005, background): “A Appendix: on the connections with the Clarke gradient Several notions of gradients have been introduced in convex and non-smooth analysis: see for instance [1], [4], [11], [12] and [33].”
Nonsmooth analysis on smooth manifolds (2007, background): “The books and articles [2, 14, 25, 26, 29, 42, 45, 49, 56, 58, 75, 76] provide powerful tools and present interesting perspectives to the field of nonsmooth and variational analysis.”
Risk-averse dynamic programming for Markov decision processes (2010, background): “Let us quickly review basic concepts of continuity of multifunctions (see [3] for an extensive presentation).”