Fekete-Szego Inequality for Certain Subclasses of Analytic Functions Related with Crescent-Shaped Domain and Application of Poison Distribution Series

The purpose of this paper is to define a new class of analytic, normalized functions in the open unit disk D = {z:z EC and 121< 1} subordinating with crescent shaped regions, and to derive certain coefficient estimates a2 , az and Fekete-Szegö inequality for f e Ma(a, b, 1). A similar result have been done for the function f-1. Further application of our results to certain functions defined by convolution products with a normalized analytic function is given, in particular we obtain Fekete inequalities for certain subclasses of functions defined through Poisson distribution series.