A mean value property for pairs of integrals.
A measure-theoretic characterization of the Henstock-Kurzweil integral revisited
In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral.
A method for constructing orthonormal bases for non-archimedean Banach spaces of continuous functions
A method for solving fuzzy Fredholm integral equations of the second kind.
A minimum energy condition of 1-dimensional periodic sphere packing.
A monotonicity criterion for arbitrary functions
A monotonicity property of power means.
A monotonicity property of ratios of symmetric homogeneous means.
A Monte Carlo Method for High Dimensional Integration.
A more generalized Gronwall-like integral inequality with applications.
A multidimensional analogue of the Denjoy-Perron-Henstock-Kurzweil integral.
A multidimensional integration by parts formula for the Henstock-Kurzweil integral
It is shown that if is of bounded variation in the sense of Hardy-Krause on , then is of bounded variation there. As a result, we obtain a simple proof of Kurzweil’s multidimensional integration by parts formula.
A multidimensional Taylor's theorem with minimal hypothesis
A multiple Hardy-Hilbert integral inequality with the best constant factor.
A multiple Hilbert-type integral inequality with the best constant factor.
A multiplicative embedding inequality in Orlicz--Sobolev spaces.
A necessary and sufficient condition for continuity of additive functions
A necessary condition for HK-integrability of the Fourier sine transform function
The paper is concerned with integrability of the Fourier sine transform function when , where is the space of bounded variation functions vanishing at infinity. It is shown that for the Fourier sine transform function of to be integrable in the Henstock-Kurzweil sense, it is necessary that . We prove that this condition is optimal through the theoretical scope of the Henstock-Kurzweil integration theory.
A new algorithm for approximating the least concave majorant
The least concave majorant, , of a continuous function on a closed interval, , is defined by We present an algorithm, in the spirit of the Jarvis March, to approximate the least concave majorant of a differentiable piecewise polynomial function of degree at most three on . Given any function , it can be well-approximated on by a clamped cubic spline . We show that is then a good approximation to . We give two examples, one to illustrate, the other to apply our algorithm.
A new and more powerful concept of the PU-integral