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

Document Type: Regular Paper


1 Department of Mathematics, Rajiv Gandhi University, Rono Hills, Doimukh 791112, Arunachal Pradesh, India

2 Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

3 Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India


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.