New type of Lacunary Orlicz Difference Sequence Spaces Generated By Infinite Matrices

Ayhan Esi, Bipan Hazarika, Ayten Esi

The main purpose of this paper is to introduce the spaces $\widehat{W}^0_\theta[A,M,\Delta,p]$, $\widehat{W}_\theta[A,M,\Delta,p]$ and $\widehat{W}^\infty_\theta[A,M,\Delta,p]$ generated by infinite matrices defined by Orlicz functions. Some properties of these spaces are discussed. Also we introduce the concept of $\widehat{S}_\theta[A,\Delta]$-statistical convergence and derive some results between the spaces $\widehat{S}_\theta[A,\Delta]$ and $\widehat{w}_\theta[A,\Delta]$. Further, we study some geometrical properties such as order continuous, the Fatou property and the Banach--Saks property of the new space $\widehat{w}^\infty_{\theta\alpha}[A,\Delta,p]$. Finally, we introduce the notion of $\widehat{S}_\theta[A,\Delta]$-statistical convergence of order $\alpha$ of real number sequences and obtain some inclusion relations between the set of $\widehat{S}[A,\Delta]$-statistical convergence of order $\alpha$.