Recently in The restricted sumsets in finite abelian groups it is proved that
Suppose that $k \geq 2$ and $A$ is a non-empty subset of a finite abelian group $G$ with $|G| > 1$. Then the cardinality of the restricted sumset $k^\wedge A := \{a_1 + · · · + a_k : a_1, \ldots , a_k \in A, a_i \neq a_j \hspace{.1cm} \text{for} \hspace{.1cm} i \neq j\}$ is at least min$\{p(G), k|A| − k^2 + 1\}$, where $p(G)$ denotes the least prime divisor of $|G|$.
What can we say if we consider $G$ as an ordered group? Is there any literature that has dealt with restricted sumsets in ordered groups?
