SOME PROPERTIES OF STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC-CONJUGATE POINTS

HASSOON AL-AMIRI ； DAN COMAN ； PETRU T. MOCANU

《International Journal of Mathematics and Mathematical Sciences》 1995卷 (1995/12) Pp. 469-474

https://doi.org/10.1155/S0161171295000597

摘要

Let A be tile class of all analytic functions in the unit disk U such that f(0)=f’(0)−1=0. A function f ∈ A is called starlike with respect to 2n symmetric-conjugate points if Re zf’(z)/fn(z)＞0 for z ∈ U, where(The equation is abbreviated) ω=exp(2πi/n]. This class is denoted by S_n^*, and was studied in [1]. A sufficient condition for starlikeness with respect to symmetric-conjugate points is obtained. In addition, images of some subclasses of S_n^* under the integral operator I: A→A, I(f)=F where(The equation is abbreviated)and g ∈ A is given are determined.

關鍵字

symmetric-conjugate points ； starlike ； differential subordinations ； integral operator ； strongly starlike ； α-convex