A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES

Abstract

In this study, we use generalized difference sequences $\Delta ^{m}x=(\Delta ^{m}x_{k})=(\Delta ^{m-1}x_{k}-\Delta ^{m-1}x_{k+1})$ to obtain more general results about weak convergence and we investigate the concept of $\Delta ^{m} \mathcal{I-}$weak convergence where $m\in \mathbb{N} $. We also define weak $\Delta^{m}\mathcal{I-}$limit points and weak $ \Delta^{m}\mathcal{I-}$cluster points.