?im-Lacunary Statistical Convergence of Order ?

Abstract

The purpose of this work is to introduce the concepts of Delta(m)(i)-lacunary statistical convergence of order alpha and lacunary strongly (Delta(m)(i), p)-convergence of order alpha. We establish some connections between lacunary strongly (Delta(m)(i), p)-convergence of order alpha and Delta(m)(i)-lacunary statistical convergence of order alpha. It is shown that if a sequence is lacunary strongly (Delta(m)(i), p)-summable of order alpha then it is Delta(m)(i)-lacunary statistically convergent of order alpha.