The aim of this paper is to study the problem of coefficient bounds for a newly defined subclass of p-valent analytic functions. Many known results appear as special consequences of our work.

In this paper, we introduce new general integral operators. New sufficient conditions for these operators to be p-valently starlike, p-valently close-to-convex, uniformly p-valent close-to-convex and strongly starlike of order γ (0 < γ ≤ 1) in the open unit disk are obtained.

The purpose of the present paper is to establish some interesting results on the generalizations of quasi-Hadamard product of functions belonging to the classes of p-valent starlike and p-valent convex functions of order α in the open unit disc U. Our results improve the results of previous authors to the case when r and s are any positive real numbers such that s > 1. It is worth noting that t...

4. The Components of the Fatou set 4.1. The types of domains of normality 4.2. The classification of periodic components 4.3. The role of the singularities of the inverse function 4.4. The connectivity of the components of the Fatou set 4.5. Wandering domains 4.6. Classes of functions without wandering domains 4.7. Baker domains 4.8. Classes of functions without Baker domains 4.9. Completely in...

In the present paper, we introduce and investigate some properties of two subclasses $ Lambda_{n}( lambda , beta ) $ and $ Lambda_{n}^{+}( lambda , beta ) $;  meromorphic and starlike  functions of order $ beta $. In particular, several inclusion relations, coefficient estimates, distortion theorems and covering theorems are proven here for each of these function classes.

Nevanlinna theory [Ne] was created to give a quantitative measure of the value distribution for meromorphic functions, for instance to measure the extent to which they approximate a finite number of points. We view a meromorphic function as a holomorphic map ƒ : C —• P into the projective line. The theory has various higher dimensional analogues, of which we shall later consider maps ƒ : C —• X...

In this paper, by meromorphic functions we will always mean meromorphic functions in the complex plane C. We adopt the standard notations of the Nevanlinna theory of meromorphic functions as explained in [6]. It will be convenient to let E denote any set of positive real numbers of finite linear measure, not necessarily the same at each occurrence. For a non-constant meromorphic function h, we ...