The objective of the present paper is to introduce a certain general class P ( p , α , β ) ( p ∈ N = { 1 , 2 , 3 , … } ,  0 ≤ α < p   and   β ≥ 0 ) of p -valent analytic functions in the open unit disk U and we prove that if f ∈ P ( p , α , β ) then J p , c ( f ) , defined by J p , c ( f ) = c + p z c ∫ 0 z t c − 1 f ( t ) d t     ( c ∈ N ) belongs to P ( p , α , β ) . We also investigate inclusion properties of the class P ( p , α , β ) . Furthermore, we examine some properties for a class T p ( α , β ) of analytic functions with negative coefficients.