On infinite derivatives of continuous functions
On integrability in F-spaces
Some usual and unusual properties of the Riemann integral for functions x : [a,b] → X where X is an F-space are investigated. In particular, a continuous integrable -valued function (0 < p < 1) with non-differentiable integral function is constructed. For some class of quasi-Banach spaces X it is proved that the set of all X-valued functions with zero derivative is dense in the space of all continuous functions, and for any two continuous functions x and y there is a sequence of differentiable...
On -differentiability and difference properties of functions
On Lipschitz conditions for ordinary differential equations in Fréchet spaces
We will give an existence and uniqueness theorem for ordinary differential equations in Fréchet spaces using Lipschitz conditions formulated with a generalized distance and row-finite matrices.
On local derivatives
On nonconvex subdifferential calculus in Banach spaces.
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