On representation of functionals of local type by differential forms
On rough norms on Banach spaces
On sets of non-differentiability of Lipschitz and convex functions
We observe that each set from the system (or even ) is -null; consequently, the version of Rademacher’s theorem (on Gâteaux differentiability of Lipschitz functions on separable Banach spaces) proved by D. Preiss and the author is stronger than that proved by D. Preiss and J. Lindenstrauss. Further, we show that the set of non-differentiability points of a convex function on is -strongly lower porous. A discussion concerning sets of Fréchet non-differentiability points of continuous convex...
On some new characterizations of weakly compact sets in Banach spaces
We show several characterizations of weakly compact sets in Banach spaces. Given a bounded closed convex set C of a Banach space X, the following statements are equivalent: (i) C is weakly compact; (ii) C can be affinely uniformly embedded into a reflexive Banach space; (iii) there exists an equivalent norm on X which has the w2R-property on C; (iv) there is a continuous and w*-lower semicontinuous seminorm p on the dual X* with such that p² is everywhere Fréchet differentiable in X*; and as a...
On stability of classes of Lipschitz mappings generated by compact sets of linear mappings.
On strong continuity of derivatives of mappings
On the Approximation of Hausdorff Upper Semi-Continuous Correspondences.
On the behaviour of solutions to the nonlinear elliptic Neumann problem in unbounded domains
The asymptotic behaviour is studied for minima of regular variational problems with Neumann boundary conditions on noncompact part of boundary.
On the differentiability of Lipschitz mappings in Fréchet spaces
On the differentiability of multivalued mappings. I.
On the differentiability of multivalued mappings. II.
On the differentiation of convex functions
On the differentiation of convex functions in finite and infinite dimensional spaces
On the embedding theorem
On the Fréchet differentiability of distance functions
On the geometric characterization of differentiability. I.
On the geometric characterization of differentiability. II.
On the multiplicity points of monotone operators on separable Banach spaces
On the open mapping principle and convex multivalued mappings
On the range of the derivative of a real-valued function with bounded support
We study the set f’(X) = f’(x): x ∈ X when f:X → ℝ is a differentiable bump. We first prove that for any C²-smooth bump f: ℝ² → ℝ the range of the derivative of f must be the closure of its interior. Next we show that if X is an infinite-dimensional separable Banach space with a -smooth bump b:X → ℝ such that is finite, then any connected open subset of X* containing 0 is the range of the derivative of a -smooth bump. We also study the finite-dimensional case which is quite different. Finally,...