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Statistical summability through a lacunary sequence in locally solid Riesz spaces. (English) Zbl 1283.40005

Summary: We introduce the concepts of lacunary statistical \({\tau}\)-convergence, lacunary statistically \({\tau}\)-bounded sequences and lacunary statistically \({\tau}\)-Cauchy sequences in the framework of locally solid Riesz spaces. We also define a new type of convergence.

MSC:

40A35 Ideal and statistical convergence
40G15 Summability methods using statistical convergence
46A40 Ordered topological linear spaces, vector lattices
40J05 Summability in abstract structures
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