The statistical unbounded topological convergence was studied and investigated with respect to the solid topology in locally Riesz spaces. In this paper, we introduce order spaces by developing a topology-free technique on Moreover, give some relations other kinds of convergences.

We first show that a bounded linear operator $ T $ on a real Banach space $ E $ is quasicompact (Riesz, respectively) if and only if $T': E_{mathbb{C}}longrightarrow E_{mathbb{C}}$ is quasicompact  (Riesz, respectively), where the complex Banach space $E_{mathbb{C}}$ is a suitable complexification of $E$ and $T'$ is the complex linear operator on $E_{mathbb{C}}$ associated with $T$. Next, we pr...

In this note we characterize cr-finite Riesz measures that allow one to approximate measurable functions by continuous functions in the sense of Lusin's theorem. We call such measures Lusin measures and show that not all cr-finite measures are Lusin measures. It is shown that if a topological space X is either normal or countably paracompact, then every measure on A' is a Lusin measure. A count...

in this paper we consider the so called a vector metric space, which is a generalization of metric space, where the metric is riesz space valued. we prove some common fixed point theorems for three mappings in this space. obtained results extend and generalize well-known comparable results in the literature.