On a class of starlike functions defined in a halfplane

Let D = {z: Re z < 0} and let S*(D) be the class of univalent functions normalized by the conditions ${\displaystyle \underset{D\ni z\to \infty }{lim}(f\left(z\right)-z)=a}$, a a finite complex number, 0 ∉ f(D), and mapping D onto a domain f(D) starlike with respect to the exterior point w = 0. Some estimates for |f(z)| in the class S*(D) are derived. An integral formula for f is also given.