Young Jae Sim

Notes on analytic functions with a bounded positive real part

For real α and β such that 0≤α<1<β, we denote by S(α,β) the class of normalized analytic functions f such that α<Re{zf′(z)/f(z)}<β in . We find some properties, including inclusion properties, Fekete-Szegö problem and coefficient problems of inverse functions.MSC:30C45, 30C55.

A Subclass of Meromorphic Close-to-Convex Functions of Janowski's Type

We introduce a subclass Σ(𝐴,𝐵)(−1≤𝐵<𝐴≤1) of functions which are analytic in the punctured unit disk and meromorphically close-to-convex. We obtain some coefficients bounds and some argument and convolution properties belonging to this class.

On Certain Classes of Convex Functions

For real numbers and such that , we denote by the class of normalized analytic functions which satisfy the following two sided-inequality: where denotes the open unit disk. We find some relationships involving functions in the class . And we estimate the bounds of coefficients and solve the Fekete-Szego problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

A CERTAIN SUBCLASS OF JANOWSKI TYPE FUNCTIONS ASSOCIATED WITH κ-SYMMETRIC POINTS

Abstract. We introduce a subclass S (k)s (A,B) (−1 ≤ B < A ≤ 1)of functions which are analytic in the open unit disk and close-to-convexwith respect to k-symmetric points. We give some coefficient inequalities,integral representations and invariance properties of functions belongingto this class. 1. IntroductionLet A denote the class of functions which are analytic in the open unit diskUand normalized by f(0) = 0 and f ′ (0) = 1. Also let S denote the subclassof A consisting of all functions which are univalent in U.Let f(z) and F(z) be analytic in U. Then we say that the function f(z) issubordinate to F(z) in U, if there exists an analytic function w(z) in U suchthat |w(z)| ≤ 1 and f(z) = F(w(z)), denote by f ≺ F or f(z) ≺ F(z). IfF(z) is univalent in U, then the subordination is equivalent to f(0) = F(0) andf(U) ⊂ F(U).Now, we denote by S ∗ (A,B) and C(A,B) the subclasses of A as follows:(1) S ∗ (A,B) =ˆf ∈ A :zf ′ (z)f(z)≺1+Az1+Bz,z ∈ U˙and(2) C(A,B) =ˆf ∈ A : ∃g ∈ S ∗ (A,B) such thatzf

Geometric Properties of Lommel Functions of the First Kind

In the present paper, we find sufficient conditions for starlikeness and convexity of normalized Lommel functions of the first kind using the admissible function methods. Additionally, we investigate some inclusion relationships for various classes associated with the Lommel functions. The functions belonging to these classes are related to the starlike functions, convex functions, close-to-convex functions and quasi-convex functions.

The Pre-Schwarzian Norm Estimate for Analytic Concave Functions

Let denote the open unit disk and let denote the class of normalized univalent functions which are analytic in . Let be the class of concave functions , which have the condition that the opening angle of at infinity is less than or equal to , . In this paper, we find a sufficient condition for the Gaussian hypergeometric functions to be in the class . And we define a class , , which is a subclass of and we find the set of variabilities for the functional for . This gives sharp upper and lower estimates for the pre-Schwarzian norm of functions in . We also give a characterization for functions in in terms of Hadamard product.