We prove an Ekelandâ€™s type vector variational principle for monotonically semicontinuous mappings with perturbations given by a convex bounded subset of directions multiplied by the distanceâ€¦ (More)

The problem of finding an optimal insurerâ€™s strategy of purchasing reinsurance is considered under the standard deviation calculation principles. It is assumed that the strategy must satisfy severalâ€¦ (More)

For twice smooth functions, the symmetry of the matrix of second partial derivatives is automatic and can be seen as the symmetry of the Jacobian matrix of the gradient mapping. For nonsmoothâ€¦ (More)

Sufficient conditions for an equilibrium of maximal monotone operator to be in a given set are provided. This partially answers to a question posed in [10].

For a boundedly generated drop [a,E] (a property which holds, for instance, whenever E is bounded), where a belongs to a real Banach space X and E âŠ‚ X is a nonempty convex set, we show that for everyâ€¦ (More)

It is known that the subdifferential of a lower semicontinuous convex function f over a Banach space X determines this function up to an additive constant in the sense that another function of theâ€¦ (More)