Generalized difference sequence spaces of fractional order defined by Orlicz functions

Abstract

The main purpose of this paper is to introduce the concepts of Δ^{α}-lacunary statistical convergence of order β (0<β≤1) with the fractional order of α and Δ^{α}-lacunary strongly convergence of order β (0<β≤1) with the fractional order of α. We establish some connections between Δ^{α}-lacunary strongly convergence of order β and Δ^{α}-lacunary statistical convergence of order β.