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

Authors : Hafize GÜMÜŞ, Mikail ET

Pages : 113-122

View : 15 | Download : 5

Publication Date : 2017-04-01

Article Type : Research Paper

Abstract :In this study, we use generalized difference sequences $\Delta ^{m}x=insert ignore into journalissuearticles values(\Delta ^{m}x_{k});=insert ignore into journalissuearticles values(\Delta ^{m-1}x_{k}-\Delta ^{m-1}x_{k+1});$ 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