A converse inequality of Hölder type.
A converse of Minkowski's type inequalities.
A converse of the Arsenin–Kunugui theorem on Borel sets with σ-compact sections
Let f be a Borel measurable mapping of a Luzin (i.e. absolute Borel metric) space L onto a metric space M such that f(F) is a Borel subset of M if F is closed in L. We show that then is a set for all except countably many y ∈ M, that M is also Luzin, and that the Borel classes of the sets f(F), F closed in L, are bounded by a fixed countable ordinal. This gives a converse of the classical theorem of Arsenin and Kunugui. As a particular case we get Taĭmanov’s theorem saying that the image of...
A converse to some inequalities and approximations in the theory of Stieltjes and stochastic integrals, and for nth derivatives
A counter example on common periodic points of functions.
A counterexample to a Fedorenko statement.
A counterexample to the strong real Jocobian conjecture.
A criterion for unimodality.
A curious property of series involving terms of generalized sequences.
A Daniell integral approach to nonstandard Kurzweil-Henstock integral
A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results.
A Darboux property of -approximate partial derivatives.
A d.c. function need not be difference of convex functions
In [2] a delta convex function on is constructed which is strictly differentiable at but it is not representable as a difference of two convex function of this property. We improve this result by constructing a delta convex function of class which cannot be represented as a difference of two convex functions differentiable at 0. Further we give an example of a delta convex function differentiable everywhere which is not strictly differentiable at 0.
A dense subsemigroup of S(R) generated by two elements
A derivative to match the v-integral.
A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities
Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.
A descriptive definition of a BV integral in the real line
A descriptive characterization of a Riemann type integral, defined by BV partition of unity, is given and the result is used to prove a version of the controlled convergence theorem.
A descriptive definition of some multidimensional gauge integrals
A direct approach to one variable noncommutative calculus
A direct extension of Meller's calculus.
A discontinuous function with a connected closed graph