The decomposition of functions of bounded ϰ-variation into differences of ϰ-decreasing functions
The Denjoy extension of the Riemann and McShane integrals
In this paper we study the Denjoy-Riemann and Denjoy-McShane integrals of functions mapping an interval into a Banach space It is shown that a Denjoy-Bochner integrable function on is Denjoy-Riemann integrable on , that a Denjoy-Riemann integrable function on is Denjoy-McShane integrable on and that a Denjoy-McShane integrable function on is Denjoy-Pettis integrable on In addition, it is shown that for spaces that do not contain a copy of , a measurable Denjoy-McShane integrable...
The Difference Between the Product and the Convolution Product of Distribution Functions in
The Dirichlet-Jordan theorem for the Henstock-Fourier transform.
The divergence theorem and Perron integration with exceptional sets
The dual of the cone of all convex functions on a vector space.
The Dual of the Cone of All Convex Functions on a Vector Space. (Short Communication).
The dual of the space of functions of bounded variation
In the paper, we show that the space of functions of bounded variation and the space of regulated functions are, in some sense, the dual space of each other, involving the Henstock-Kurzweil-Stieltjes integral.
The dynamics of complex polynomials and automorphisms of the shift.
The extension of majorization inequalities within the framework of relative convexity.
The Extremal Convex Functions.
The Feigenbaum functional equation and periodic points.
The Feigenbaum functional equation and periodic points. (Short Communication).
The foam drainage equation with time and space-fractional derivatives solved by the adomian method.
The Fourier transform in Lebesgue spaces
For each () it is shown that the Fourier transform is the distributional derivative of a Hölder continuous function. For each , a norm is defined so that the space of Fourier transforms is isometrically isomorphic to . There is an exchange theorem and inversion in norm.
The fractal dimension of invariant subsets for piecewise monotonic maps on the interval.
The fundamental solutions for fractional evolution equations of parabolic type.
The fundamental solutions for fractional evolution equations of parabolic type.
The fundamental theorem for the -integral on more general sets and a corresponding divergence theorem with singularities
The fundamental theorem of calculus for Lebesgue integral.