Starlikeness Of Certain Integral Operators And Properties Of A Subclass Of Close To Convex Functions

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Date
2017-02
Authors
Chung, Yao Liang
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Publisher
Universiti Sains Malaysia
Abstract
The present dissertation investigates the sufficient conditions for an analytic function to be starlike in the open unit disk D and some properties of certain subclass of close-to-convex functions. A brief survey of the basic concepts and results from the classical theory of analytic univalent functions are given. Sufficient conditions for analytic functions satisfying certain third-order differential inequalities to be starlike in D is derived. As a consequence, conditions for starlikeness of functions defined by triple integral operators are obtained. Connections are also made to earlier known results. Furthermore, a new subclass of close-to-convex functions is introduced and studied. Some interesting results are obtained such as inclusion relationships, an estimate for the Fekete-Szegö functional for functions belonging to the class, coefficient estimates, and a sufficient condition.
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Keywords
Starlikeness of certain integral operators , subclass of close to convex functions
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