On a Theorem of N.Th. Varopoulos.
On an application of a Newton-like method to the approximation of implicit functions
On boundedly-convex functions on pseudo-topological vector spaces.
On conability of singlevalued mappings
On convex functions in c0(w1).
It is proved that no convex and Fréchet differentiable function on c0(w1), whose derivative is locally uniformly continuous, attains its minimum at a unique point.
On De Blasi's differentiation theory for multifunctions
On derivations on certain function spaces and their relation to the differential operator. (Über Derivationen auf gewissen Funktionenräumen und deren Beziehung zum Differentiationsoperator.)
On differentiability properties of Lipschitz functions on a Banach space with a Lipschitz uniformly Gâteaux differentiable bump function
We improve a theorem of P.G. Georgiev and N.P. Zlateva on Gâteaux differentiability of Lipschitz functions in a Banach space which admits a Lipschitz uniformly Gâteaux differentiable bump function. In particular, our result implies the following theorem: If is a distance function determined by a closed subset of a Banach space with a uniformly Gâteaux differentiable norm, then the set of points of at which is not Gâteaux differentiable is not only a first category set, but it is even -porous...
On differentiation of metric projections in finite dimensional Banach spaces
On Fréchet differentiability of convex functions on Banach spaces
Equivalent conditions for the separability of the range of the subdifferential of a given convex Lipschitz function defined on a separable Banach space are studied. The conditions are in terms of a majorization of by a -smooth function, separability of the boundary for or an approximation of by Fréchet smooth convex functions.
On full derivatives
On functions with vanishing local derivative
On Gateaux differentiable bump functions
It is shown that the order of Gateaux smoothness of bump functions on a wide class of Banach spaces with unconditional basis is not better than that of Fréchet differentiability. It is proved as well that in the separable case this order for Banach lattices satisfying a lower p-estimate for 1≤ p < 2 can be only slightly better.
On Hadamard differentiability
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.