%0 Journal Article
%T Hankel determinant for certain class of analytic function defined by generalized derivative operator
%A Ma'moun Harayzeh Al-Abbadi
%A Maslina Darus
%J Tamkang Journal of Mathematics
%D 2012
%I Tamkang University
%R 10.5556/j.tkjm.43.2012.445-453
%X The authors in cite{mam1} have recently introduced a new generalised derivatives operator $ mu_{lambda _1 ,lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $mu_{lambda _1 ,lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ mathcal{H}_{lambda _1 ,lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=left{{z,inmathbb{C}:,left| z ight|,<,1}  ight}$ and satisfy egin{equation*} {mathop{ m Re} olimits} left( {mu _{lambda _1 ,lambda _2 }^{n,m} f(z)} ight)^prime > 0,,,,,,,,,,(z in U). end{equation*} This paper focuses on attaining sharp upper bound for the functional $left| {a_2 a_4 - a_3^2 } ight|$ for functions $f(z)=z+ sumlimits_{k = 2}^infty {a_k ,z^k }$ belonging to the class $mathcal{H}_{lambda _1 ,lambda _2 }^{n,m}$.
%K Differential operator
%K Analytic functions
%K superordination
%U http://journals.math.tku.edu.tw/index.php/TKJM/article/view/517