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The main purpose of the present paper is to introduce and study some weaker forms of continuity in bitopological ordered spaces. Such as pairwise I-continuous maps, pairwise D-continuous maps, pairwise B-continuous maps, pairwise I-open maps, pairwise D-open maps, pairwise B-open maps, pairwise I-closed maps, pairwise D-closed maps, and pairwise B-closed maps. 

ordered topological space, increasing sets, decreasing sets, continuous maps, maps, pairwise continuous maps, pairwise open maps, pairwise closed maps.