On Janowski starlike functions (Q2471970)

Applying the fractional calculus to analytic functions \(f(z)\) defined on the open unit disc \(U\) with \(f(0)=0\) and \(f^\prime(0)=1\) [cf. \textit{W. Janowski}, Bull. Acad. Pol. Sci., Sér. Sci. Math. Astron. Phys. 21, 17--25 (1973; Zbl 0252.30021)], the authors introduce a new fractional operator \(D^\lambda f(z)\) and define a subclass of the class of functions \(f(z)=z+\sum_{n=2}^\infty a_nz^n\) analytic in \(U\) associated with Janowski functions and investigate some of their properties.