International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 3, Pages 175-180

Lacunary statistical convergence and inclusion properties between lacunary methods

Jinlu Li

Department of Mathematics, Shawnee State University, Portsmouth 45662, OH, USA

Received 6 August 1998

Copyright © 2000 Jinlu Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A lacunary sequence is an increasing integer sequence θ={kr} such that krkr1 as r. A sequence x is called sθ-convergent to L provided that for each ϵ>0, limr(1/(krkr1)){the number ofkr1<kkr:|xkL|ϵ}=0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.