Title data
Baier, Robert ; Farkhi, Elza:
Discrete Filippovtype stability for onesided Lipschitzian difference inclusions.
In: Feichtinger, Gustav ; Kovacevic, Raimund M. ; Tragler, Gernot
(ed.):
Control Systems and Mathematical Methods in Economics : Essays in Honor of Vladimir M. Veliov. 
Cham
: Springer
,
2018
.  pp. 2755
.  (Lecture Notes in Economics and Mathematical Systems
; 687
)
ISBN 9783319751689
DOI: https://doi.org/10.1007/9783319751696_3
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Project information
Project financing: 
Andere The Hermann Minkowski Center for Geometry at Tel Aviv University, Israel 

Abstract in another language
We state and prove Filippovtype stability theorems for discrete difference inclusions obtained by the Euler discretization of a differential inclusion with perturbations in the set of initial points, in the righthand side and in the state variable. We study the cases in which the righthand side of the inclusion is not necessarily Lipschitz, but satisfies a weaker onesided Lipschitz (OSL) or strengthened onesided Lipschitz (SOSL) condition. The obtained estimates imply stability of the discrete solutions for infinite number of fixed time steps if the OSL constant is negative and the perturbations are bounded in certain norms. We show a better order of stability for SOSL righthand sides and apply our theorems to estimate the distance from the solutions of other difference methods, as for the implicit Euler scheme to the set of solutions of the Euler scheme. We also prove a discrete relaxation stability theorem for the considered difference inclusion, which also extends a theorem of G. Grammel (2003) from the class of Lipschitz maps to the wider class of OSL ones.
Further data
Item Type:  Article in a book 

Refereed:  Yes 
Keywords:  onesided Lipschitz condition; strengthened onesided Lipschitz condition; setvalued Euler’s method; differential inclusions 
Subject classification:  Mathematics Subject Classification Code: 34A60 47H05 (39A30 54C60) 
Institutions of the University:  Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  31 Oct 2018 12:38 
Last Modified:  31 Oct 2018 12:38 
URI:  https://eref.unibayreuth.de/id/eprint/46180 
Available Versions of this Item

Discrete Filippovtype stability for onesided Lipschitzian difference inclusions. (deposited 14 Oct 2017 21:00)
 Discrete Filippovtype stability for onesided Lipschitzian difference inclusions. (deposited 31 Oct 2018 12:38) [Currently Displayed]