A Class of Univalent Functions with Real Coefficients

Abstract

In this paper, we study class $$\mathcal {S}^+$$ of univalent functions f such that $$\frac{z}{f(z)}$$ has real and positive coefficients. For such functions, we give estimates of the Fekete–Szegő functional and sharp estimates of their initial coefficients and logarithmic coefficients. Also, we present necessary and sufficient conditions for $$f\in \mathcal {S}^+$$ to be starlike of order 1 / 2.