On Janowski Starlike Functions

Abstract

For analytic functions f(z) in the open unit disc 𝕌 with f(0)=0 and f′(0)=1, applying the fractional calculus for f(z), a new fractional operator Dλf(z) is introduced. Further, a new subclass 𝒮λ∗(A,B) consisting of f(z) associated with Janowski function is defined. The objective of the present paper is to discuss some interesting properties of the class 𝒮λ∗(A,B).