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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.
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.