Fekete-Szegő problem for subclasses of generalized uniformly starlike functions with respect to symmetric points. (English) Zbl 1340.30087

Yagmur, Nihat; Orhan, Halit

Math. Bohem. 139, No. 3, 485-509 (2014).

In the first part the authors obtain upper bounds for the Fekete-Szegő functional \(| \mu \, a^{2}_{2}-a_{3} | \) for a new class \(k-UST^{n}_{\lambda, \mu}(s,t,\gamma)\) of analytic functions defined by using a Salagean type differential operator. They also study in the same sense the class \(k-UST^{n, g}_{\lambda, \mu}(s,t,\gamma)\) and a subclass of it denoted by \(k-UST^{n, \tau}_{\lambda, \mu}(s,t,\gamma)\) defined by using the fractional derivative and the Hadamard product.

Reviewer: Mugur Acu (Sibiu)

MSC:

30C45	Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
30C50	Coefficient problems for univalent and multivalent functions of one complex variable

Keywords:

Fekete-Szegő problem; Sakaguchi function; uniformly starlike function; symmetric point