A computer proof of Turán's inequality.
A concept of absolute continuity and a Riemann type integral
We present a descriptive definition of a multidimensional generalized Riemann integral based on a concept of generalized absolute continuity for additive functions of sets of bounded variation.
A concise proof for properties of three functions involving the exponential function.
A condition implying boundedness and VMO for a function f
Some boundedness and VMO results are proved for a function f integrable on a cube , starting from an integral bound.
A condition of Busemann-Feller type for the derivation of integrals of functions in the class Φ (L).
A conjecture of Schoenberg.
A conjecture on general means.
A constructive integral equivalent to the integral of Kurzweil
We slightly modify the definition of the Kurzweil integral and prove that it still gives the same integral.
A continous version of Orlicz-Pettis theorem via vector-valued Henstock-Kurzweil integrals
We show that a Pettis integrable function from a closed interval to a Banach space is Henstock-Kurzweil integrable. This result can be considered as a continuous version of the celebrated Orlicz-Pettis theorem concerning series in Banach spaces.
A continuous and a discrete variant of Wirtinger's inequality.
A continuum of minimal pairs of compact convex sets which are not connected by translations.
A contour view on uninorm properties
Any given increasing function is completely determined by its contour lines. In this paper we show how each individual uninorm property can be translated into a property of contour lines. In particular, we describe commutativity in terms of orthosymmetry and we link associativity to the portation law and the exchange principle. Contrapositivity and rotation invariance are used to characterize uninorms that have a continuous contour line.
A convergence theory of some methods of integration.
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.