On Certain Generalized Bazilevic type Functions Associated with Conic Regions
Journal: Sahand Communications in Mathematical Analysis (Vol.17, No. 4)Publication Date: 2020-11-01
Authors : Khalida Inayat Noor; Shujaat Ali Shah;
Page : 13-23
Keywords : Conic regions; Bazilevic function; Bounded boundary rotation; Hankel determinant; Univalent functions;
Abstract
Let $f$ and $g$ be analytic in the open unit disc and, for $alpha ,$ $beta geq 0$, let
begin{align*}
Jleft( alpha ,beta ,f,gright) & =frac{zf^{prime }(z)}{f^{1-alpha
}(z)g^{alpha }(z)}+beta left( 1+frac{zf^{prime prime }(z)}{f^{prime
}(z)}right) -beta left( 1-alpha right) frac{zf^{prime }(z)}{f(z)}
& quad -alpha beta frac{zg^{prime }(z)}{g(z)}text{.}
end{align*}
The main aim of this paper is to study the class of analytic functions which map $Jleft( alpha ,beta ,f,gright) $ onto conic regions. Several interesting problems such as arc length, inclusion relationship, rate of growth of coefficient and Growth rate of Hankel determinant will be discussed.
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Last modified: 2021-11-03 14:29:36