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On statistically lq-complete and c0s in measure convergences of sequences of measurable functions

Papanastasiou N., Papachristodoulos C., Dimitriou X.

Journal of Applied Analysis

2016

Vol. 22, nr 2

163--168

We introduce and study s-lq-complete and c0s-μ convergences, and we obtain a new result regarding statistical convergences of sequences of measurable functions.

Modes of ideal continuity and the additive property in the Riesz space setting

Boccuto A., Dimitriou X., Papanastassiou N., Wilczyński W.

Journal of Applied Analysis

2014

Vol. 20, nr 1

41--53

In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the (AP)-property for ideals of an abstract set Λ. Finally we pose some open problems.

Unconditional convergence in lattice groups with respect to ideals

Boccuto A., Dimitriou X., Papanastassiou N.

Commentationes Mathematicae

2010

Vol. 50, [Z] 2

161-174

We deal with unconditional convergence of series and some special classes of subsets of N.