On the Coefficients of Some Subclasses of Univalent Functions

In this paper we consider the class L_c*(,,) consisting of analytic and univlent functions with negative coefficients and with fixed second coefficient. The object of the present paper is to show coefficient estimates, convex linear combinations, some distortion theoems and radii of starlikeness and convexity for f(z) in the class L_c*(,,). The results are generalized to families with finitely many fixed coefficients.AMS Subject Classification (1991) 30C45     

MEROMORPHIC p-VALENT FUNCTION WITH FIXED SECOND NEGATIVE COEFFICIENTS

In this paper we consider the class ∑[p, α, β, k, c] consisting of analytic functions with negative coefficients and fixed second coefficient. The object of the present paper is to give coefficient estimates,convex linear combinations, some distortion theorems and radii of starlikeness and convexity for f (z) in the class ∑[p, α, β, k, c].     

Geometric properties of the Cassinian metric

In this paper we prove a sharp distortion property of the Cassinian metric under Möbius transformations of a punctured ball onto another punctured ball. The paper also deals with discussion on local convexity properties of the Cassinian metric balls in proper subdomains of . Inclusion properties of the Cassinian metric balls with other hyperbolic‐type metric balls are also investigated. In particular, several conjectures are also stated in response to sharpness of the inclusion relations.     

Some Properties of Two Subclasses of Analytic Functions

This paper discusses some properties of two classes Vk[α,β] and Rk[α,β ]. Sharp distortion theorem and radius of convexity and starlikeness are obtained. Hadamard product of functions in the classes are also studied.     

On order of strongly starlikeness in the class of uniformly convex functions

In this paper we consider the order of strongly starlikeness in the classes uniformly convex functions.     

Ordinary differential operator and some of its applications to certain meromorphically p-valent functions

By making use of the well-known assertions given in Miller and Mocanu (1978) [13] and Nunokawa (1993) [14], certain theorems concerning p-valently meromorphic (strongly) starlike and (strongly) convex functions obtained in this investigation are firstly proved and then their certain consequences which will be interesting or important for analytic and geometric function theory are pointed out.     

On a generalization of starlike functions

In this paper, we mainly study the order of $q$-starlikeness of the well-known basic hypergeometric function. In addition, we discuss the Bieberbach-type problem and the second order Hankel determinant for a generalized class of starlike functions.     

On the order of starlikeness of the shifted Gauss hypergeometric function

We determine for several ranges of real parameters the order of starlikeness of the shifted Gauss hypergeometric function and we give some consequences of our results, in particular some mapping properties of the Carlson-Shaffer convolution operator.     

关于强星像函数类的一个子类

引入了强星像函数类的一个子类Ｓ（α，β，ρ，σ，Ａ，Ｂ），讨论了它的从属关系、包含关系、星像阶数和强星像阶数以及积分表示定理等，所得结果推广了一些作者的相关工作。