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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.

MSC:

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