International Journal of Mathematics and Mathematical Sciences
Volume 23 (2000), Issue 3, Pages 175-180
doi:10.1155/S0161171200001964
Lacunary statistical convergence and inclusion properties between lacunary methods
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.
Abstract
A lacunary sequence is an increasing integer sequence θ={kr} such that kr−kr−1→∞ as
r→∞. A sequence x is called sθ-convergent to
L provided that for each ϵ>0, limr(1/(kr−kr−1)){the number of kr−1<k≤kr:|xk−L|≥ϵ}=0. In this paper, we study the
general description of inclusion between two arbitrary lacunary
sequences convergent.