The statistically unbounded ? -convergence on locally solid Riesz spaces

Abstract

A sequence $(x_n)$ in a locally solid Riesz space (E, ? ) is said to be statistically unbounded ? -convergent to x ? E if, for every zero neighborhood U , 1/n I {k ? n : |xk ? x| ? u /? U}I ? 0 as n ? ?In this paper, we introduce the concept of the st-u? -convergence and give the notions of st-u? -closed subset, st-u? -Cauchy sequence, st-u? -continuous and st-u? -complete locally solid vector lattice. Also, we give some relations between the order convergence and the st-u? -convergence.