All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 142 Next

Displaying 2821 – 2840 of 4562

Showing per page

On some properties of Hamel bases and their applications to Marczewski measurable functions

François Dorais, Rafał Filipów, Tomasz Natkaniec (2013)

Open Mathematics

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 Separately Increasing Functions from [0,1]ⁿ into a Banach Space

Artur Michalak (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

We say that a function f from [0,1] to a Banach space X is increasing with respect to E ⊂ X* if x* ∘ f is increasing for every x* ∈ E. A function f : [ 0 , 1 ] m → X is separately increasing if it is increasing in each variable separately. We show that if X is a Banach space that does not contain any isomorphic copy of c₀ or such that X* is separable, then for every separately increasing function f : [ 0 , 1 ] m → X with respect to any norming subset there exists a separately increasing function g : [ 0 , 1 ] m → ℝ such that the sets of points of discontinuity...

On some representations of almost everywhere continuous functions on ℝ m

Ewa Strońska (2006)

Colloquium Mathematicae

It is proved that the following conditions are equivalent: (a) f is an almost everywhere continuous function on ℝ m ; (b) f = g + h, where g,h are strongly quasicontinuous on ℝ m ; (c) f = c + gh, where c ∈ ℝ and g,h are strongly quasicontinuous on ℝ m .

On some shift invariant integral operators, univariate case

George A. Anastassiou, Heinz H. Gonska (1995)

Annales Polonici Mathematici

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...

Currently displaying 2821 – 2840 of 4562