ON GENERALIZED DIFFERENCE LACUNARY STATISTICAL CONVERGENCE

A lacunary sequence is an increasing integer sequence = (kr) such that k0 =0, kr kr 1 ! 1 as r ! 1. A sequence x is called S ( m ) convergent to L provided that for each > 0, limr(kr kr 1) 1 {the number of kr 1 < k kr : | m xk L| } = 0, where m xk = m 1 xk m 1 x k+1. The purpose of this paper is to introduce the concept of m lacunary statistical convergence and m -lacunary strongly convergence and examine some properties of these sequence spaces. We establish some connections between m -lacunary strongly convergence and m -lacunary statistical convergence. It is shown that if a sequence is m -lacunary strongly convergent then it is m -lacunary statistically convergent. We also show that the space S ( m ) may be represented as a (f,p, )( m ) space.