Abstract
The main object of this paper is to study some properties of certain subclass of analytic functions with negative coefficients defined by a linear operator in the open unit disc. These properties include the coefficient estimates, closure properties, distortion theorems and integral operators.
Highlights
Let be the class of analytic functions in the open unit discLet n denote the class of functions f z normalized by f z z ak zk, n : (1)k n 1 which are analytic in the open unit disc
The main object of this paper is to study some properties of certain subclass of analytic functions with negative coefficients defined by a linear operator in the open unit disc
The result is sharp with the extremal function fn 1 given in (14)
Summary
Our work here motivated by Catas [2], who introduced an operator on as follows: Dlm, f k 1. The generalized Salagean derivative operator introduced by Al-Oboudi [7]: D0m, 1,1 f z. Following the earlier investigations by [8] and [9], we define n, -neighborhood of a function f z n by. Let n denote the subclass of n consisting of functions which satisfy. We denote by n the subclass of n consisting of all such functions [10]. By using Dlm, a,b we will define a new class of starlike functions. Definition 1.2 Let. we shall use the same method by [17] to establish certain coefficient estimates relating to the new introduced class
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