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A Class of Starlike Functions Defined by the Dziok-Srivastava Operator
Silverman, Herb,Murugusundaramoorhty, Gangadharan,Vijaya, Kaliappan Department of Mathematics 2009 Kyungpook mathematical journal Vol.49 No.1
A comprehensive class of starlike univalent functions defined by Dziok-Srivastava operator is introduced. Necessary and sufficient coefficient bounds are given for functions in this class to be starlike. Further distortion bounds, extreme points and results on partial sums are investigated.
Upper bounds of second Hankel determinant for universally prestarlike functions
Om Ahuja,Murugesan Kasthuri,GANGADHARAN. MURUGUSUNDARAMOORTHY,Kaliappan Vijaya 대한수학회 2018 대한수학회지 Vol.55 No.5
In \cite{Rusche1,Rusche2} the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain $\mathbb{C}\backslash \lbrack 1,\infty )$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order $\alpha $ with $\alpha \leq 1$ and we obtain upper bounds of the second Hankel determinant $|a_{2}a_{4}-a_{3}^{2}|$ for such functions.
UPPER BOUNDS OF SECOND HANKEL DETERMINANT FOR UNIVERSALLY PRESTARLIKE FUNCTIONS
Ahuja, Om,Kasthuri, Murugesan,Murugusundaramoorthy, Gangadharan,Vijaya, Kaliappan Korean Mathematical Society 2018 대한수학회지 Vol.55 No.5
In [12,13] the researchers introduced universally convex, universally starlike and universally prestarlike functions in the slit domain ${\mathbb{C}}{\backslash}[1,{\infty})$. These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we introduce universally prestarlike generalized functions of order ${\alpha}$ with ${\alpha}{\leq}1$ and we obtain upper bounds of the second Hankel determinant ${\mid}a_2a_4-a^2_3{\mid}$ for such functions.