Sanabria, Rosas and Carpintero [7] introduced the notions of ΛsI-sets and ΛsI-closed sets using ideals on topological spaces. Given an ideal I on a topological space (X, τ), a subset A ⊂ X is said to be ΛsI-closed if A = U∩F where U is a ΛsI-set and F is a τ*-closed set. In this work we use sets that are complements of ΛsI-closed sets, which are called ΛsI-open, to characterize new variants of continuity namely ΛsI-continuous, quasi- ΛsI-continuous y ΛsI-irresolute functions.