a function is said to be bi-univalent on the open unit disk d if both the function and its inverse are univalent in d. not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. in this paper we use the faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

A function is said to be bi-univalent on the open unit disk D if both the function and its inverse are univalent in D. Not much is known about the behavior of the classes of bi-univalent functions let alone about their coefficients. In this paper we use the Faber polynomial expansions to find coefficient estimates for four well-known classes of bi-univalent functions which are defined by subord...

assume that $mathbb{d}$ is the open unit disk. applying ozaki's conditions, we consider two classes of locally univalent, which denote by $mathcal{g}(alpha)$ and $mathcal{f}(mu)$ as follows begin{equation*}  mathcal{g}(alpha):=left{fin mathcal{a}:mathfrak{re}left( 1+frac{zf^{prime prime }(z)}{f^{prime }(z)}right)

in this paper we introduce and investigate a certain subclass of univalentfunctions which are analytic in the unit disk u.such results as coecientinequalities. the results presented here would provide extensions of those givenin earlier works.

making use of an extended fractional differintegral operator ( introduced recently by patel and mishra), we introduce a new subclass of multivalent analytic functions and investigate certain interesting properties of this subclass.

The main result shows that a small perturbation of a univalent function is again a univalent function, hence a univalent function has a neighbourhood consisting entirely of univalent functions. For the particular choice of a linear function in the hypothesis of the main theorem, we obtain a corollary which is equivalent to the classical Noshiro–Warschawski–Wolff univalence criterion. We also pr...

in the present paper, we prove subordination, superordination and sandwich-type properties of a certain integral operators for univalent functions on open unit disc, moreover the special behavior of this class is investigated.

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.