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

Abstract

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