λ-fractional properties of generalized Janowski functions in the unit disc

Abstract

For analytic function f(z) = z + a2z 2 + · · · in the open unit disc D, a new fractional operator Dλf(z) is defined. Applying this fractional operator Dλf(z) and the principle of subordination, we give new proofs for some classical results concerning the class S ∗ λ (A, B, α) of functions f(z).