In this paper we investigate a subclass M(α) of the class of starlike functions in the unit disk |z| < 1. M(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f′(0) − 1 = 0 that satisfy the condition 1+α−π2sinα<Re{zf'(z)f(z)}<1+α2sinα(z∈Δ) The class M(α) was introduced by Kargar et al. [Complex Anal. Oper. Theory 11: 1639–1649, 2017]. In this paper some basic geometric properties of the class M(α) are investigated. Among others things, coefficients estimates and bound are given for the Fekete-Szegö functional associated with the k–th root transform [f(z^k)]^1/k. Also a certain subclass of bi–starlike functions is introduced and the bounds for the initial coe?cients are obtained.

Keywords: analytic functions, starlike and bistarlike functions, subordination, Fekete-Szegö, inequality.