A Subclass of Uniformly Convex Functions and a Corresponding Subclass of Starlike Functions with Fixed Second Coefficient Defined by Carlson and Shaffer Operator
نویسنده
چکیده
Abstract The main objective of this paper is to obtain necessary and sufficient condition for a subclass of uniformly convex functions and corresponding subclass of starlike functions with fixed second coefficient defined by Carlson and Shaffer operator for the function f(z) in UCT (α, β). Furthermore, we obtain extreme points, distortion bounds and closure properties for f(z) in UCT (α, β) by fixing second coefficient.
منابع مشابه
A 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 کاملA New Subclass of Uniformly Convex Functions and a Corresponding Subclass of Starlike Functions with Fixed Second Coefficient
Making use of Linear operator theory, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain coefficient estimates distortion bounds, closure theorems and extreme points for functions belonging to this new class. The results are generalized to families with fixed finitely ma...
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 کاملUniformly Starlike and Convex Functions with Negative Coefficients
Let A(ω) be the class of analytic functions of the form: f(z) = (z − ω) + ∞ ∑ k=2 ak(z − ω) defined on the open unit disk U = {z : |z| < 1} normalized with f(ω) = 0, f ′(ω)−1 = 0 and ω is an arbitrary fixed point in U. In this paper, we define a subclass of ω − α − uniform starlike and convex functions by using a more generalized form of Ruschewey derivative operator. Several properties such as...
متن کاملOn a Subclass of Multivalent β-Uniformly Starlike and Convex Functions defined by a Linear Operator
AbstractIn this paper we introduce the subclass K(μ, γ, η, α, β) of β-uniformly convex and β-uniformly starlike functions which are analytic and multivalent with negative coefficients defined by using fractional calculus operators. Characterization property exhibited by the functions in the class and the results of modified Hadamard product are discussed. Connections with the popular subclasses...
متن کامل