The Convex Hull of a Typical Compact Set.
The counterpart of Fan's inequality and its related results.
The Covering Principle for Darboux Baire 1 functions
We show that the Covering Principle known for continuous maps of the real line also holds for functions whose graph is a connected subset of the plane. As an application we find an example of an approximately continuous (hence Darboux Baire 1) function f: [0,1] → [0,1] such that any closed subset of [0,1] can be translated so as to become an ω-limit set of f. This solves a problem posed by Bruckner, Ceder and Pearson [Real Anal. Exchange 15 (1989/90)].
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 Denjoy-Clarkson property with respect to Hausdorff measures for the gradient mapping of functions of several variables
We construct a differentiable function () such that the set is a nonempty set of Hausdorff dimension . This answers a question posed by Z. Buczolich.
The Difference Between the Product and the Convolution Product of Distribution Functions in
The Differentiable Functions from R into R n
In control engineering, differentiable partial functions from R into Rn play a very important role. In this article, we formalized basic properties of such functions.
The Dirichlet-Jordan theorem for the Henstock-Fourier transform.
The discrete version of Ostrowski's inequality in normed linear spaces.
The distance between subdifferentials in the terms of functions
For convex continuous functions defined respectively in neighborhoods of points in a normed linear space, a formula for the distance between and in terms of (i.eẇithout using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly...
The distribution of unbounded random sets and the multivalued strong law of large numbers in nonreflexive Banach spaces.
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 equal variable method.
The extension of a cyclic inequality to the symmetric form.
The extension of majorization inequalities within the framework of relative convexity.