\(\lambda\)-fractional properties of generalized Janowski functions in the unit disc. (English) Zbl 1224.30022

Çağlar, Mert; Polatoğlu, Yaşar; Yavuz, Emel

Mat. Vesn. 60, No. 3, 165-171 (2008).

Authors’ abstract: “For an analytic function \(f(z)=z+a_2z^2+\cdots\) in the open unit disc \(\mathbb D\), a new fractional operator \(D^\lambda f(z)\) is defined. Applying this fractional operator \(D^\lambda f(z)\) and the principle of subordination, we give new proofs for some classical results concerning the class \(\mathcal S_\lambda^*(A,B,\alpha)\) of functions \(f(z)\).”

Reviewer: Vesna Manojlović (Beograd)

MSC:

30C45

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Keywords:

starlike function; fractional integral; fractional derivative; distortion theorem