A Class of Analytic Functions Defined by the Carlson-shaffer Operator
نویسندگان
چکیده
The Carlson-Shaffer operator L(a, c)f = φ(a, c) ∗ f, where f(z) = z+ a2z + · · · is analytic in the unit disk E = {z : |z| < 1} and φ(a, c; z) is an incomplete beta function, is used to define the class T (a, c). An analytic function f belongs to T (a, c) if L(a, c)f is starlike in E. The object of the present paper is to derive some properties of functions f in the class T (a, c).
منابع مشابه
Subordination Results for a Class of Analytic Functions Defined by a Linear Operator
In this paper, we derive several interesting subordination results for certain class of analytic functions defined by the linear operator L(a, c)f(z) which introduced and studied by Carlson and Shaffer [2].
متن کاملA Subclass of Analytic Functions Associated with Hypergeometric Functions
In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.
متن کاملOn Certain Analytic Functions Defined by Carlson Shaffer Operator
In this paper, we study the new subclasses of analytic functions in the unit disk E by using Carlson Shaffer operator and generalized Janowski functions. These new analytic classes relates with the concept of functions of bounded radius rotation and bounded Mocanu variation. Inclusion results and convolution invariant property are investigated.
متن کاملThe Fekete – Szegö problem for a class of analytic functions defined by Carlson – Shaffer operator
In the present investigation we solve Fekete–Szegö problem for the generalized linear differential operator. In particular, our theorems contain corresponding results for various subclasses of strongly starlike and strongly convex functions.
متن کاملSome Properties of Analytic Functions Defined by a Linear Operator
The object of the present paper is to derive some properties of analytic functions defined by the Carlson Shaffer linear operator L(a, c)f(z) .
متن کامل