A constructive integral equivalent to the integral of Kurzweil
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
Curves in Banach spaces which allow a parametrization or a parametrization with finite convexity
We give a complete characterization of those (where is a Banach space) which allow an equivalent parametrization (i.e., a parametrization whose derivative has bounded variation) or a parametrization with bounded convexity. Our results are new also for . We present examples which show applicability of our characterizations. For example, we show that the and parametrization problems are equivalent for but are not equivalent for .
Die richtigen Räume für Analysis im Unendlich-Dimensionalen.
Existence theory for integrodifferential equations and Henstock-Kurzweil integral in Banach spaces.
Flett's mean value theorem in topological vector spaces.
Functions of class Ck without derivatives.
We describe a general axiomatic way to define functions of class Ck, k ∈ N∪{∞} on topological abelian groups. In the category of Banach spaces, this definition coincides with the usual one. The advantage of this axiomatic approach is that one can dispense with the notion of norms and limit procedures. The disadvantage is that one looses the derivative, which is replaced by a local linearizing factor. As an application we use this approach to define C∞ functions in the setting of graded/super manifolds....
Gâteaux differentiable functions are somewhere Fréchet differentiable
Mean value theorems for some linear integral operators.
Monotone and convex -algebra valued functions.
On Some Properties of Separately Increasing Functions from [0,1]ⁿ into a Banach Space
We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function with respect to any norming subset there exists a separately increasing function such that the sets of points of discontinuity...
Riemann type integrals for functions taking values in a locally convex space
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given.
Seminorm generating relations and their Minkowski functionals.
Some remarks about a notion of rearrangement
The weak McShane integral
We present a weaker version of the Fremlin generalized McShane integral (1995) for functions defined on a -finite outer regular quasi Radon measure space into a Banach space and study its relation with the Pettis integral. In accordance with this new method of integration, the resulting integral can be expressed as a limit of McShane sums with respect to the weak topology. It is shown that a function from into is weakly McShane integrable on each measurable subset of if and only if...
Weaker forms of continuity and vector-valued Riemann integration
It was proved by Kadets that a weak*-continuous function on [0,1] taking values in the dual of a Banach space X is Riemann-integrable precisely when X is finite-dimensional. In this note, we prove a Fréchet-space analogue of this result by showing that the Riemann integrability holds exactly when the underlying Fréchet space is Montel.