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1
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Metric subregularity of order q and the solving of inclusions

100%
Gaydu M., Geoffroy M., Jean-Alexis C.
Open Mathematics
|
2011
|
tom 9
|
nr 1
147-161
EN
We consider some metric regularity properties of order q for set-valued mappings and we establish several characterizations of these concepts in terms of Hölder-like properties of the inverses of the mappings considered. In addition, we show that even if these properties are weaker than the classical notions of regularity for set-valued maps, they allow us to solve variational inclusions under mild assumptions.
2
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Multivalued backward stochastic differential equations with time delayed generators

76%
Diomande B., Maticiuc L.
Open Mathematics
|
2014
|
tom 12
|
nr 11
1624-1637
EN
Our aim is to study the following new type of multivalued backward stochastic differential equation: $$\left\{ \begin{gathered} - dY\left( t \right) + \partial \phi \left( {Y\left( t \right)} \right)dt \ni F\left( {t,Y\left( t \right),Z\left( t \right),Y_t ,Z_t } \right)dt + Z\left( t \right)dW\left( t \right), 0 \leqslant t \leqslant T, \hfill \\ Y\left( T \right) = \xi , \hfill \\ \end{gathered} \right.$$ where ∂φ is the subdifferential of a convex function and (Y t, Z t):= (Y(t + θ), Z(t + θ))θ∈[−T,0] represent the past values of the solution over the interval [0, t]. Our results are based on the existence theorem from Delong & Imkeller, Ann. Appl. Probab., 2010, concerning backward stochastic differential equations with time delayed generators.
3
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A-monotone nonlinear relaxed cocoercive variational inclusions

76%
Verma R.
Open Mathematics
|
2007
|
tom 5
|
nr 2
386-396
EN
Based on the notion of A - monotonicity, a new class of nonlinear variational inclusion problems is presented. Since A - monotonicity generalizes H - monotonicity (and in turn, generalizes maximal monotonicity), results thus obtained, are general in nature.
4
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Equilibrium shapes of charged droplets and related problems: (mostly) a review

76%
Goldman M., Ruffini B.
Geometric Flows
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2017
|
tom 2
|
nr 1
EN
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations in the functional. The original contribution of this note is twofold. First, we prove existence of an optimal distribution of charge for a conducting drop subject to an external electric field. Second, we prove that there exists no optimal conducting drop in this setting.
5
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An extragradient iterative scheme by viscosity approximation methods for fixed point problems and variational inequality problems

64%
Petruşel A., Yao J.-C.
Open Mathematics
|
2009
|
tom 7
|
nr 2
335-347
EN
In this paper, we introduce a new iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for an α-inverse-strongly-monotone, by combining an modified extragradient scheme with the viscosity approximation method. We prove a strong convergence theorem for the sequences generated by this new iterative process.
6
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Generalized bi-quasi-variational inequalities for quasi-pseudo-monotone type II operators on compact sets

52%
Chowdhury M., Tan K.-K.
Open Mathematics
|
2010
|
tom 8
|
nr 1
158-169
EN
In this paper, the authors prove some existence results of solutions for a new class of generalized bi-quasi-variational inequalities (GBQVI) for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators defined on compact sets in locally convex Hausdorff topological vector spaces. In obtaining these results on GBQVI for quasi-pseudo-monotone type II and strongly quasi-pseudo-monotone type II operators, we shall use Chowdhury and Tan’s generalized version [3] of Ky Fan’s minimax inequality [7] as the main tool.
7
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Subdifferential inclusions and quasi-static hemivariational inequalities for frictional viscoelastic contact problems

46%
Migórski S.
Open Mathematics
|
2012
|
tom 10
|
nr 6
1953-1968
EN
We survey recent results on the mathematical modeling of nonconvex and nonsmooth contact problems arising in mechanics and engineering. The approach to such problems is based on the notions of an operator subdifferential inclusion and a hemivariational inequality, and focuses on three aspects. First we report on results on the existence and uniqueness of solutions to subdifferential inclusions. Then we discuss two classes of quasi-static hemivariational ineqaulities, and finally, we present ideas leading to inequality problems with multivalued and nonmonotone boundary conditions encountered in mechanics.
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