  , T For real numbers  and  such that 0 1      , we denote by   the class of normalized analytic functions which satisfy     Re f z     z   , T   , where denotes the open unit disk. We find some relationships involving functions in the class      . And we estimate the bounds of coefficients and solve Fekete-Szegö problem for functions in this class. Furthermore, we...

Motivated and stimulated especially by the work of Xu et al. [1], in this paper, we introduce and discuss an interesting subclass ( ) , Σ ψ λ of analytic and bi-univalent functions defined in the open unit disc  . Further, we find estimates on the coefficients 2 a and 3 a for functions in this subclass. Many relevant connections with known or new results are pointed out.

We give a criterion for q-valent analytic functions in the unit disk to belong to Q K , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nonde-creasing function K : [0, ∞) → [0, ∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Q p spaces are obtained. 1. Introduction....

The aim of this paper is two-fold. First, to give a direct proof for the already established result of Styer which states that a univalent geometrically starlike function f is a univalent annular starlike function if f is bounded. Second, to show that the boundedness condition of f is necessary, thus disproving a conjecture of Styer.

1 Presented by We construct a function f (z), univalent and starlike in the unit disc, with some interesting geometric and analytic properties. It turns out that its convolutions f * λn with a specific class of univalent polynomials λn(z) are not subordinate to the function itself. This provides a counterexample to a result of Greiner and Ruscheweyh.