Geometric ZWEIER Convergent Lacunary Sequence Spaces

Abstract

The main purpose of this paper is to introduce lacunary strong geometric zweier convergent sequence spaces $N_{\theta }^{0} \left[Z\left(G\right)\right]$, $N_{\theta } \left[Z\left(G\right)\right]$, $N_{\theta }^{\infty } \left[Z\left(G\right)\right]$consisting of all sequences $x=\left(x_{k} \right)$such that $\left[Z\left(G\right)\right]x$ are in the spaces $N_{\theta }^{0} ,N_{\theta } {\rm and\; }N_{\theta }^{\infty } $ respectively, which are normed. We prove certain topological properties of these spaces and compute their lacunary stastical zweier convergence.