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On some double almost lacunary sequence spaces defined by Orlicz functions. (English) Zbl 1094.42004
The well-known concepts (with respect to an Orlicz function) almost convergence, convergence in the Pringsheim sense of double sequences of complex numbers, strong summability, and almost lacunary statistical convergence are combined to define some new sequence spaces. They generalize several sequence spaces that have extensively been studied in the past. The results are some basic set inclusions, and relations between the summability methods that arise in the context of the new spaces. The proofs use the standard methods and techniques, with the obvious modifications and adaptations, from the special cases.
MSC:
42A55Lacunary series of trigonometric and other functions; Riesz products
40C05Matrix methods in summability