- Konuralp Journal of Mathematics
- Vol: 5 Issue: 1
- A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES
A DIFFERENT VIEWPOINT ABOUT THE WEAK CONVERGENCE VIA IDEALS AND $\Delta ^{m}$ SEQUENCES
Authors : Hafize Gümüş, Mikail Et
Pages : 113-122
View : 15 | Download : 3
Publication Date : 2017-04-01
Article Type : Research
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.Keywords : Weak convergence, $mathcal{I}-$convergence, $Delta ^{m}$ sequences, $mathcal{I}-$limit points, $mathcal{I}-$cluster points.