On Algebraic Curves over Real Closed Fields. II.
On almost continuous additive functions
On almost periodicity defined via non-absolutely convergent integrals
We investigate some properties of the normed space of almost periodic functions which are defined via the Denjoy-Perron (or equivalently, Henstock-Kurzweil) integral. In particular, we prove that this space is barrelled while it is not complete. We also prove that a linear differential equation with the non-homogenous term being an almost periodic function of such type, possesses a solution in the class under consideration.
On almost quasicontinuity
The concept of almost quasicontinuity is investgated in this paper in several directions (e.g. the relation of this concept to other generalizations of continuity is described, various types of convergence of sequences of almost quasicontinuous function are studied, a.s.o.).
On an Abstract Formulation of Regularity
On an equation of linear iteration.
On an inequality of G. Gruss
On an inequality of G. H. Hardy.
On an inequality of Gauss.
In this note we prove a new extension and a converse of an inequality due to Gauss.
On an Inequality of P.m. Vasić and R.r. Janić
On approximate Dini derivates and one-sided approximate derivatives of arbitrary functions
On approximate symmetric derivative
On approximation of Baire functions by Darboux functions
On - associated comonotone functions
We give a positive answer to two open problems stated by Boczek and Kaluszka in their paper [1]. The first one deals with an algebraic characterization of comonotonicity. We show that the class of binary operations solving this problem contains any strictly monotone right-continuous operation. More precisely, the comonotonicity of functions is equivalent not only to -associatedness of functions (as proved by Boczek and Kaluszka), but also to their -associatedness with being an arbitrary strictly...
On belated differentiation and a characterization of Henstock-Kurzweil-Ito integrable processes
The Henstock-Kurzweil approach, also known as the generalized Riemann approach, has been successful in giving an alternative definition to the classical Itô integral. The Riemann approach is well-known for its directness in defining integrals. In this note we will prove the Fundamental Theorem for the Henstock-Kurzweil-Itô integral, thereby providing a characterization of Henstock-Kurzweil-Itô integrable stochastic processes in terms of their primitive processes.
On Borsík's problem concerning quasiuniform limits of Darboux quasicontinuous functions
On boundedness and discontinuity of additive functions
On bounds of the range of ordered variates II.
On Cauchy-Frullani Integrals
On certain formulas for the multivariable hypergeometric functions.