Let denote the open unit disc and let be holomorphic and injective in . We further assume that is unbounded and is a convex domain. In this article, we consider the Taylor coefficients of the normalized expansion
and we impose on such functions the second normalization . We call these functions concave schlicht functions, as the image of is a concave domain. We prove that the sharp inequalities
are valid. This settles a conjecture formulated in .