On Certain Subclasses of Analytic Functions Defined by Differential Subordination

Hesam Mahzoon

doi:10.1155/2011/103521

Abstract

We introduce and study certain subclasses of analytic functions which are defined by differential subordination. Coefficient inequalities, some properties of neighborhoods, distortion and covering theorems, radius of starlikeness, and convexity for these subclasses are given.

Highlights

We introduce and study certain subclasses of analytic functions which are defined by differential subordination
A function f ∈ T j is said to be in the class Tj n, m, A, B, λ if
A function f ∈ T j is said to be in the class Rj n, A, B, λ if it satisfies z∈U, 3.1 where −1 ≤ B < A ≤ 1, λ ≥ 1 and n ∈ N0

Summary

Introduction

F z z − akzk, ak ≥ 0, j ∈ N {1, 2, . . .} , kj[1] defined in the open unit disc U {z ∈ C : |z| < 1}. Let Ω be the class of functions ω analytic in U such that ω 0 0, |ω z | < 1. A function f ∈ T j is said to be in the class Tj n, m, A, B, λ if. A function f ∈ T j is said to be in the class Pj n, A, B, λ if it satisfies. In view of condition 1.4 , we get the required result of Theorem 3.6. A function f ∈ T j is said to be in the class Kλj n, m, A, B, C, D if it satisfies fz gz. This implies that f ∈ Kλj n, m, A, B, C, D

Distortion and Covering Theorems

Radii of Starlikeness and Convexity