Turkish Journal of Mathematics
DOI
10.3906/mat-1912-37
Abstract
A sequence $(x_n)$ in a locally solid Riesz space $(E,\tau)$ is said to be statistically unbounded $\tau$-convergent to $x\in E$ if, for every zero neighborhood $U$, $\frac{1}{n}\big\lvert\{k\leq n:\lvert x_k-x\rvert\wedge u\notin U\}\big\rvert\to 0$ as $n\to\infty$. In this paper, we introduce the concept of the $st$-$u_\tau$-convergence and give the notions of $st$-$u_\tau$-closed subset, $st$-$u_\tau$-Cauchy sequence, $st$-$u_\tau$-continuous and $st$-$u_\tau$-complete locally solid vector lattice. Also, we give some relations between the order convergence and the $st$-$u_\tau$-convergence.
Keywords
Statistically $u_\tau$-convergence, statistically $u_\tau$-cauchy, locally solid Riesz space, order convergence, Riesz space
First Page
949
Last Page
956
Recommended Citation
AYDIN, ABDULLAH
(2020)
"The statistically unbounded $\tau$-convergence on locally solid Riesz spaces,"
Turkish Journal of Mathematics: Vol. 44:
No.
3, Article 22.
https://doi.org/10.3906/mat-1912-37
Available at:
https://journals.tubitak.gov.tr/math/vol44/iss3/22
