Generalized difference paranormed statistically convergent sequences defined by Orlicz function in a locally convex space. (English) Zbl 1066.40005

This paper introduces the generalized difference paranormed spaces of statistically convergent, statistically null, bounded statistically convergent and bounded statistically null sequences over a seminormed space. The author describes the history, definitions and previous results and then introduces the new notions and proves several propositions and theorems concerning these spaces. A nice example discussing the relation with distribution theory is also included. Overall an interesting and excellently written paper.


40A05 Convergence and divergence of series and sequences
46A45 Sequence spaces (including Köthe sequence spaces)