$\Delta^{m}$-lacunary Statistical Convergence of Order $\alpha$ Defined by a Modulus Function

Abstract

In this paper, we introduce the concepts of lacunary $\Delta^{m}$-statistically convergent sequence of order $\alpha$ and strongly
$N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences of order $\alpha$ are introduced. Some inclusion relations between the set of lacunary $\Delta^{m}$-statistically convergent sequences of order $\alpha$ and strongly $N_{\theta}^{\alpha}(\Delta^{m},f,p)$-summable sequences of order $\alpha$ and the relations between two arbitrary lacunary sequences are discussed.