On ω-approximately continuous Denjoy-Steiltjes integral
Operator-valued functions of bounded semivariation and convolutions
The abstract Perron-Stieltjes integral in the Kurzweil-Henstock sense given via integral sums is used for defining convolutions of Banach space valued functions. Basic facts concerning integration are preseted, the properties of Stieltjes convolutions are studied and applied to obtain resolvents for renewal type Stieltjes convolution equations.
Ordinary differential equations the solution of which are -functions
Orthogonally additive functionals on
In this paper we give a representation theorem for the orthogonally additive functionals on the space in terms of a non-linear integral of the Henstock-Kurzweil-Stieltjes type.
Passage of the limit through the double Denjoy integral.
Path-wise solutions of stochastic differential equations driven by Lévy processes.
In this paper we show that a path-wise solution to the following integral equationYt = ∫0t f(Yt) dXt, Y0 = a ∈ Rd,exists under the assumption that Xt is a Lévy process of finite p-variation for some p ≥ 1 and that f is an α-Lipschitz function for some α > p. We examine two types of solution, determined by the solution's behaviour at jump times of the process X, one we call geometric, the other forward. The geometric solution is obtained by adding fictitious time and solving an associated...
Peano Baker series convergence for matrix-valued functions of bounded variation.
Perron integral, Perron product integral and ordinary differential equations
Perron type integration on -dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence
Perron-type integration on -dimensional intervals and its properties
Pfeffer integrability does not imply -integrability
Regulated functions and the Perron-Stieltjes integral
Remarques sur l'intégrale de Riemann généralisée
Riemann-type definition of the improper integrals
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions.
Several comments on the Henstock-Kurzweil and McShane integrals of vector-valued functions
We make some comments on the problem of how the Henstock-Kurzweil integral extends the McShane integral for vector-valued functions from the descriptive point of view.
Some applications of Kurzweil-Henstock integration
Applications of ideal from Kurzweil-Henstock integration to elementary analysis on , mean value theorems for vector valued functions, l’Hospital rule, theorems of Taylor type and path independence of line integrals are discussed.
Some characterizations of the primitive of strong Henstock-Kurzweil integrable functions
In this paper we give some complete characterizations of the primitive of strongly Henstock-Kurzweil integrable functions which are defined on with values in a Banach space.
Some fixed point theorems and existence of weak solutions of Volterra integral equation under Henstock-Kurzweil-Pettis integrability
In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
Some full characterizations of the strong McShane integral
Some full characterizations of the strong McShane integral are obtained.
Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space
Using generalized absolute continuity, we characterize additive interval functions which are indefinite Henstock-Kurzweil integrals in the Euclidean space.