In this work, we introduce and study the classes of contra ΛIs-continuous, quasi-ΛIs-continuous ΛIs-irresolute functions in a topological space endowed with an ideal. We investigate relationships among these their respective characterizations. Also, analyze behavior certain notions under direct inverse images new functions.

The aim of this paper is to introduce a new class of sets called (i,j) r^g closed sets and a new class of maps called D^(i,j) continuous maps and D^(i,j)irresolute maps in bitopological spaces. Also we introduce some new spaces called (i,j) – T^1/2 , (i,j) ^T 1/2 ,*T^1/2, ^T*1/2 and ^Trg and obtain their basic properties. Mathematics Subject Classification: 54A10