Coefficient Estimates and Other Properties for a Class of Spirallike Functions Associated with a Differential Operator

Abstract

For 0 <= eta < 1, 0 <= lambda < 1, -pi/2 < gamma < pi/2, 0 <= beta <= alpha, and m is an element of N boolean OR {0}, a new class S-alpha,beta(m)(eta, gamma, lambda) of analytic functions defined by means of the differential operator D-alpha,beta(m), is introduced. Our main object is to provide sharp upper bounds for Fekete- Szego problem in S-alpha,beta(m)(eta, gamma, lambda). We also find sufficient conditions for a function to be in this class. Some interesting consequences of our results are pointed out.