Some inclusion results for lacunary statistical convergence in locally solid Riesz spaces

Abstract

Recently, Mohiuddine and Alghamdi introduced the notion of lacunary statistical convergence in a locally solid Riesz space and established some results related to this concept. In this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a Tauberian theorem to the locally solid Riesz space setting are proved. Further, we introduce the concepts of -summable and statistically lacunary convergence in locally solid Riesz space and establish a relationship between them.