The notion of Î³- b -open sets in generalized topological spaces was introduced and studied by Sivagami [5] in 2008: By using the notion of Î¼-b-open sets, we introduce and study (b; Î¼Y )-continuous functions, Î¼-b-kernel and (Î¼X; Î¼Y)-b-open functions in ge-neralized topological spaces. Also some characterizations of (b; Î¼Y )-continuous functions are obtained.