Some new deterministic and random variational inequalities and their applications.
Some new existence, sensitivity and stability results for the nonlinear complementarity problem
In this work we study the nonlinear complementarity problem on the nonnegative orthant. This is done by approximating its equivalent variational-inequality-formulation by a sequence of variational inequalities with nested compact domains. This approach yields simultaneously existence, sensitivity, and stability results. By introducing new classes of functions and a suitable metric for performing the approximation, we provide bounds for the asymptotic set of the solution set and coercive existence...
Some new problems in spectral optimization
We present some new problems in spectral optimization. The first one consists in determining the best domain for the Dirichlet energy (or for the first eigenvalue) of the metric Laplacian, and we consider in particular Riemannian or Finsler manifolds, Carnot-Carathéodory spaces, Gaussian spaces. The second one deals with the optimal shape of a graph when the minimization cost is of spectral type. The third one is the optimization problem for a Schrödinger potential in suitable classes.
Some new properties in Fredholm theory, Schechter essential spectrum, and application to transport theory.
Some new results on accretive multivalued operators
Some new results on common fixed points in certain topological spaces.
Some observations concerning the non-existence of bounded differentials on weighted algebras.
Some observations on local uniform boundedness principles. II
Some operational properties of the H-R operator
Some operator inequalities
Some permanence properties of locally convex spaces defined by norm space ideals of operators
Some Perturbation Results for Analytic Semigroups.
Some problems of the spectral theory of operator pencils.
Some problems of the theory of Sobolev spaces of infinite order and of nonlinear equations
Some problems on narrow operators on function spaces
It is known that if a rearrangement invariant (r.i.) space E on [0, 1] has an unconditional basis then every linear bounded operator on E is a sum of two narrow operators. On the other hand, for the classical space E = L 1[0, 1] having no unconditional basis the sum of two narrow operators is a narrow operator. We show that a Köthe space on [0, 1] having “lots” of nonnarrow operators that are sum of two narrow operators need not have an unconditional basis. However, we do not know if such an r.i....
Some properties and applications of equicompact sets of operators
Let X and Y be Banach spaces. A subset M of (X,Y) (the vector space of all compact operators from X into Y endowed with the operator norm) is said to be equicompact if every bounded sequence (xₙ) in X has a subsequence such that is uniformly convergent for T ∈ M. We study the relationship between this concept and the notion of uniformly completely continuous set and give some applications. Among other results, we obtain a generalization of the classical Ascoli theorem and a compactness criterion...
Some properties of -convexity.
Some properties of -frames of subspaces.
Some properties of composition operators on the Dirichlet space.
Some Properties of Convex Sets Related to Fixed Points Theorems*.