On lacunary statistical convergence of double sequences in locally solid Riesz spaces

摘要

In this paper, we introduce the concepts of lacunary statistical τ- convergence,lacunary statistical r-bounded and lacunary statistical r-Cauchy for double sequences by using the double lacunary density in the framework of locally solid Riesz spaces. We also introduce the notion of S*/θ (τ)-convergence of double sequences in this setup which seems to be a quite new and interesting idea and prove some interesting results related to these notions.