Weighted Lacunary Statistical Convergence of Double Sequences in Locally Solid Riesz Spaces

Abstract

Recently, the notion of weighted lacunary statistical convergence is studied in a locally solid Riesz space for single sequences
by Ba\c{s}ar{\i}r and Konca [can be appear in Filomat, 2014]. In this work, we define and study weighted lacunary statistical $\tau$-convergence, weighted lacunary statistical
$\tau$-bounded of double sequences in locally solid Riesz spaces. We also prove some topological results related to these concepts in the
framework of locally solid Riesz spaces and give some inclusion relations.