On some spaces of lacunary convergent sequences derived by Nörlund-type mean and weighted lacunary statistical convergence

In this paper, we define some new sequence spaces of lacunary convergent sequences derived by Nörlund-type (Riesz) mean, which shall be denoted by |N‾,pr,θ| and (N‾,pr,θ), and investigate some relations between the sequence space |N‾,pr,θ| with the spaces ∣wθ∣ and |N‾,pn|. Further, we define a new concept, named weighted lacunary statistical convergence and examine some connections between this notion with the concept of lacunary statistical convergence and weighted statistical convergence. Also, some topological properties of these new sequence spaces are investigated.