1,720,975 research outputs found
Set-Valued Analysis
No full textSet-valued analysis is an important and somehow strange field, with unexpected applications in
economics, game theory, decision making, nonlinear programming, biomathematics and statistics.
This book highlights some interesting subjects in set-valued analysis, both theoretical and
practical. These topics cover various areas, such as set-valued measures and integrals, applications to
differential inclusions and decision making, and related topics in measure theory.
The papers are listed in order of publication.
Anca Croitoru, Anna Rita Sambucini, Bianca Satco Editor
Relaxation result for differential inclusions with Stieltjes derivative
No full textThe aim of this paper is to provide a Filippov-Wa\.{z}ewski Relaxation Theorem for the very general setting of Stieltjes differential inclusions. New relaxation results can be deduced for generalized differential problems, for impulsive differential inclusions with multivalued impulsive maps and possibly countable impulsive moments and also for dynamic inclusions on time scales
Stieltjes Differential Inclusions with Periodic Boundary Conditions without Upper Semicontinuity
Full text linkWe are studying first order differential inclusions with periodic boundary conditions
where the Stieltjes derivative with respect to a left-continuous non-decreasing function replaces the classical derivative. The involved set-valued mapping is not assumed to have compact and convex values, nor to be upper semicontinuous concerning the second argument everywhere, as in other related works. A condition involving the contingent derivative relative to the non-decreasing function (recently introduced and applied to initial value problems by R.L. Pouso, I.M. Marquez Albes, and J. Rodriguez-Lopez) is imposed on the set where the upper semicontinuity and the assumption to have compact convex values fail. Based on previously obtained results for periodic problems in the single-valued cases, the existence of solutions is proven. It is also pointed out that the solution set is compact in the uniform convergence topology. In particular, the existence results are obtained for periodic impulsive differential inclusions (with multivalued impulsive maps and finite or possibly countable impulsive moments) without upper semicontinuity assumptions on the right-hand side, and also the existence of solutions is derived for dynamic inclusions on time scales with periodic boundary conditions
Measure differential inclusions: existence results and minimum problems
Full text linkWe focus on a very general problem in the theory of dynamic systems, namely that of studying measure differential inclusions with varying measures.
The multifunction on the right hand side has compact non-necessarily convex values in a real Euclidean space and satisfies bounded variation hypotheses with respect to the Pompeiu excess (and not to the Hausdorff-Pompeiu distance, as usually in literature). This is possi- ble due to the use of interesting selection principles for excess bounded variation set-valued mappings.
Conditions for the minimization of a generic functional with respect to a family of measures generated by equiregulated left-continuous, nondecreasing functions and to associated solu- tions of the differential inclusion driven by these measures are deduced, under constraints only on the initial point of the trajectory
Closure properties for integral problems driven by regulated functions via convergence results
Full text linkIn this paper we give necessary and sufficient conditions for the convergence of Kurzweil–Stieltjes integrals with respect to regulated functions, using the notion of asymptotical equiintegrability. One thus generalizes several well-known convergence theorems. As applications, we provide existence and closure results for integral problems driven by regulated functions, both in single- and set-valued cases. In the particular setting of bounded variation functions driving the equations, we get features of the solution set of measure integrals problems
Special Issue on Set Valued Analysis 2021
No full textSet Valued Analysis plays an important role in the study of statistics, biology, economics, social sciences, optimal control, differential inclusions, image reconstruction and fixed point theory [...
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