Some remarks on rough statistical \(\Lambda \)-convergence of order \(\alpha \). (English) Zbl 1485.40004

Antal, Reena; Chawla, Meenakshi; Kumar, Vijay

Ural Math. J. 7, No. 1, 16-25 (2021).

Summary: The main purpose of this work is to define rough statistical \(\Lambda \)-convergence of order \(\alpha\) \((0<\alpha\leq1)\) in normed linear spaces. We have proved some basic properties and also provided some examples to show that this method of convergence is more generalized than the rough statistical convergence. Further, we have shown the results related to statistically \(\Lambda \)-bounded sets of order \(\alpha\) and sets of rough statistically \(\Lambda \)-convergent sequences of order \(\alpha \).

MSC:

40A35	Ideal and statistical convergence
40J05	Summability in abstract structures
46B99	Normed linear spaces and Banach spaces; Banach lattices

Keywords:

statistical convergence; rough statistical convergence; rough statistical limit points

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