Some spaces of weighted lacunary B^m_eta-convergent sequences defined by an Orlicz function and B^m_eta-weighted lacunary statistical convergence

Abstract

The aim of this paper is to introduce some new sequence spaces of lacunary convergent sequences combining with Riesz mean and generalized difference matrix by using an Orlicz function. Further, we define a new concept, named B_{η}^{m}-weighted lacunary statistical convergence and examine some connections between this notion with the concept of B_{η}^{m} -lacunary statistical convergence and B_{η}^{m}-weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.