Abstract. In this paper a new class of analytic functions, associated with the CarlsonShaffer operator, is investigated. The sharp estimate for the Second Hankel determinant and class preserving transforms are studied.

By making use of a multivalent analogue of the Owa-Srivastava fractional differintegral operator and its iterations, certain new families of analytic functions are introduced. Several interesting properties of these function classes, such as convolution theorems, inclusion theorems, and class-preserving transforms, are studied.