Lacunary weak statistical convergence. (English) Zbl 1249.40004

Nuray, Fatih

Math. Bohem. 136, No. 3, 259-268 (2011).

Summary: The aim of this work is to generalize lacunary statistical convergence to weak lacunary statistical convergence and \(\mathcal {I}\)-convergence to weak \(\mathcal {I}\)-convergence. We start by defining weak lacunary statistically convergent and weak lacunary Cauchy sequences. We find a connection between weak lacunary statistical convergence and weak statistical convergence.

MSC:

40A35

Ideal and statistical convergence

Keywords:

weak convergence; statistical convergence; lacunary sequence; lacunary statistical convergence