Some inequalities for a certain subclass of starlike functions

Abstract

In 2011, Sokó l (Comput. Math. Appl. 62, 611-619) introduced and studied the class SK(α) as a certain subclass of starlike functions, consists of all functions f (f (0) = 0 = f (0) − 1) which satisfy in the following subordination relation:where −3 < α ≤ 1. Also, he obtained some interesting results for the class SK(α). In this paper, some another properties of this class, including infimum of Rez , order of strongly starlikeness, the sharp logarithmic coefficients inequality and the sharp Fekete-Szegö inequality are investigated.2010 Mathematics Subject Classification. 30C45.

Coefficient and Fekete-Szegö problem estimates for certain subclass of analytic and bi-univalent functions

“…Recently, many authors have obtained the Fekete-Szegö coefficient functional associated with the k-th root transform for certain subclasses of analytic functions, see for instance [2,9,10]. In this section, we investigate this problem for the class M(α).…”