Starlike functions associated with the generalized Koebe function

Abstract

In this paper we study some properties of functions f which are analytic and normalized (i.e. f (0) = 0 = f' (0) - 1) such that satisfy the following subordination relation(zf'(z)/f(z) - 1) < z/ (1 - pz)(1 - qz),where (p, q) is an element of [-1, 1] x [-1, 1]. These types of functions are starlike related to the generalized Koebe function. Some of the features are: radius of starlikeness of order gamma is an element of [0, 1), image of f ({z : vertical bar z vertical bar < r}) where r is an element of (0, 1), radius of convexity, estimation of initial and logarithmic coefficients, and Fekete-Szego problem.