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Let D = z: Re z < 0 and let S*(D) be the class of univalent functions normalized by the conditions $li{m}_{D\ni z\to \infty }(f\left(z\right)-z)=a$, 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.