We introduce the notions of δ-I- open sets and semi δ-I-continuous functions in ideal topological spaces and investigate some of their properties. Additionally, we obtain decompositions
of semi-I-continuous functions and α-I-continuous functions by using δ-I-open sets.
We study the concepts of α-I-continuity and α-I-openness in ideal topological spaces, and obtain several characterizations and some properties of these functions. Also,
we investigate its relationship with other types of functions.