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

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.