Abstract: In this Paper using pg^b*-closed set in topological spaces we introduce a new class of sets called p generalized ^ b*-continuous functions (briefly pg^b*-continuous functions). Further the concept of almost pg^b*-continuous function and pg^b*-irresolute function are discussed.

Keywords: pg^b*-continuous function, pg^b*-irresoulte function, almost pg^b*-continuous function.