Weighted Lacunary Statistical Convergence in Locally Solid Riesz Spaces

Metin Başarir, Şükran Konca

In this paper we introduce the concepts of weighted lacunary statistical $\tau$-convergence, weighted lacunary statistical $\tau$-bounded by combining both of the definitions of lacunary sequence and N\"orlund-type mean, using a new lacunary sequence which has been defined by Basarir and Konca [3]. We also prove some topological results related to these concepts in the framework of locally solid Riesz spaces.