Characterizing Ordered Bi-Ideals in Ordered $\Gamma$-Semigroups

The notion of a $\Gamma$-semigroup was introduced by Sen [8] in 1981. We can see that any semigroup can be considered as a $\Gamma$-semigroup. The aim of this article is to study the concept of (0-)minimal and max- imal ordered bi-ideals in ordered $\Gamma$-semigroups, and give some charac- terizations of (0-)minimal and maximal ordered bi-ideals in ordered $\Gamma$- semigroups analogous to the characterizations of (0-)minimal and maxi- mal ordered bi-ideals in ordered semigroups considered by Iampan [5].