Schur geometric convexity for differences of means.
Schur-convexity of averages of convex functions.
Schur-convexity of two types of one-parameter mean values in variables.
Selection theorem in L¹
Let F be a multifunction from a metric space X into L¹, and B a subset of X. We give sufficient conditions for the existence of a measurable selector of F which is continuous at every point of B. Among other assumptions, we require the decomposability of F(x) for x ∈ B.
Seminorm generating relations and their Minkowski functionals.
Separation by monotonic functions.
Separation via quadratic functions.
Separation via quadratic functions. (Summary).
Set-valued and fuzzy stochastic integral equations driven by semimartingales under Osgood condition
We analyze the set-valued stochastic integral equations driven by continuous semimartingales and prove the existence and uniqueness of solutions to such equations in the framework of the hyperspace of nonempty, bounded, convex and closed subsets of the Hilbert space L2 (consisting of square integrable random vectors). The coefficients of the equations are assumed to satisfy the Osgood type condition that is a generalization of the Lipschitz condition. Continuous dependence of solutions with respect...
Set-valued random differential equations in Banach space
We consider the problem of the existence of solutions of the random set-valued equation: (I) , t ∈ [0,T] -a.e.; X₀ = U p.1 where F and U are given random set-valued mappings with values in the space , of all nonempty, compact and convex subsets of the separable Banach space E. Under certain restrictions on F we obtain existence of solutions of the problem (I). The connections between solutions of (I) and solutions of random differential inclusions are investigated.
Sharp power mean bounds for the combination of Seiffert and geometric means.
Singularité analytique et perturbation singulière en dimension 2
Singularité réelle isolée
Soit un germe de fonction analytique , à singularité isolée en . Nous nous proposons d’étudier le développement asymptotique des intégrales de formes , de degré , sur les fibres de . Nous montrons que ces développements asymptotiques peuvent être décrits à partir de l’action de la monodromie sur le groupe de la fibre de Milnor complexe.
Solution manifolds for systems of differential equations.
Solution of a problem of M. Katz concerning the optimization of a functional
Solutions d'un système d'équations analytiques réelles et applications
On démontre que toute solution formelle d’un système d’équations analytiques réelles (resp. polynomiales réelles) , se relève en une solution homotope à une solution analytique (resp. à une solution de Nash) aussi proche que l’on veut de pour la topologie de Krull. On utilise ce théorème pour démontrer l’algébricité (ou l’analyticité) de certains idéaux de (ou ), et aussi pour construire des déformations analytiques de germes d’ensembles analytiques en germes d’ensembles de Nash.
Some aspects of convex functions and their applications.
Some classes of infinitely differentiable functions
For nonquasianalytical Carleman classes conditions on the sequences and are investigated which guarantee the existence of a function in such that u(n)(a) = bn, bnKn+1Mn, n = 0,1,..., aJ. Conditions of coincidence of the sequences and are analysed. Some still unknown classes of such sequences are pointed out and a construction of the required function is suggested. The connection of this classical problem with the problem of the existence of a function with given trace at the boundary...
Some comparison inequalities for generalized Muirhead and identric means.
Some considerations on the monotonicity property of power means.