Chung, Yao Liang
(2022)
On A Subclass Of Analytic Functions Satisfying A Differential Inequality.
PhD thesis, Perpustakaan Hamzah Sendut.
Abstract
The present dissertation investigates complex-valued analytic functions in the open
unit disk D := {z ∈ C : |z| < 1}. A brief survey of the basic concepts and results from
the classical theory of analytic univalent functions are given. For λ ∈ (0,1], the class
of normalized analytic functions f satisfying | f ′(z)(z/ f (z))2 −1| < λ has been actively
investigated and is shown to be univalent in D. Motivated by this class, a class
of normalized analytic functions f satisfying | f ′(z)(z/ f (z))2 −μ| < λ is introduced.
Conditions on λ and μ are chosen suitably to ensure f is univalent in D. This family is
shown to be preserved under a number of elementary transformations. The necessary
and sufficient condition (in terms of integral representation) of the function f is derived.
Several important results such as finding the coefficient estimate and the bound
for the second and third Hankel determinant are determined. Lastly, some radius problems
are investigated. Connection are made with earlier results.
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