On some iterated means arising in homogenization theory
We consider iteration of arithmetic and power means and discuss methods for determining their limit. These means appear naturally in connection with some problems in homogenization theory.
On some iteration semigroups
Let be a disjoint iteration semigroup of diffeomorphisms mapping a real open interval onto . It is proved that if has a dense orbit possesing a subset of the second category with the Baire property, then for some diffeomorphism of onto the set of all reals . The paper generalizes some results of J.A.Baker and G.Blanton [3].
On some Marcus problem concerning functions possessing the derivative at points of discontinuity only
On some new fractional integral inequalities.
On some new properties of the Cantor set
On some polynomial-like inequalities of Brenner and Alzer.
On some properties of convex sequences
On Some Properties of Functions of Generalized Variation.
On some properties of functions relative to the classes of certain factor spaces
On some properties of Hamel bases and their applications to Marczewski measurable functions
We introduce new properties of Hamel bases. We show that it is consistent with ZFC that such Hamel bases exist. Under the assumption that there exists a Hamel basis with one of these properties we construct a discontinuous and additive function that is Marczewski measurable. Moreover, we show that such a function can additionally have the intermediate value property (and even be an extendable function). Finally, we examine sums and limits of such functions.
On some properties of Hamel bases connected with the continuity of polynomial functions.
On some properties of J-convex stochastic processes.
On some properties of symmetric derivatives
On some properties of the Cantor set
On some properties of the spaces of almost continuous functions.
On some shift invariant integral operators, univariate case
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and...
On some special iteration groups
On some subclasses of Darboux functions
On some subclasses of harmonic functions defined by fractional calculus.
On spaces with the ideal convergence property
Let I ⊆ P(ω) be an ideal. We continue our investigation of the class of spaces with the I-ideal convergence property, denoted (I). We show that if I is an analytic, non-countably generated P-ideal then (I) ⊆ s₀. If in addition I is non-pathological and not isomorphic to , then (I) spaces have measure zero. We also present a characterization of the (I) spaces using clopen covers.