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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.
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참고문헌 (17)
참고문헌 신청
P. L. Duren / 1983 / Univalent Functions, Grundlehren der Mathematischen Wissenschaften, Band 259 / Springer-Verlag
M. Fekete / 1933 / Eine Bemerkung Uber Ungerade Schlichte Funktionen / J. London Math. Soc. 8(2):85~89
U. Grenander / 1958 / Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences / University of California Press
A. Janteng / 2007 / Hankel determinant for starlike and convex functions / Int. J. Math. Anal. (Ruse) 1(13-16):619~625
S. K. Lee / 2013 / Bounds for the second Hankel determinant of certain univalent functions / J. Inequal. Appl. :281
M. Fekete / 1933 / Eine Bemerkung Uber Ungerade Schlichte Funktionen / J. London Math. Soc. 8(2):85~89
U. Grenander / 1958 / Toeplitz Forms and Their Applications, California Monographs in Mathematical Sciences / University of California Press
A. Janteng / 2007 / Hankel determinant for starlike and convex functions / Int. J. Math. Anal. (Ruse) 1(13-16):619~625
S. K. Lee / 2013 / Bounds for the second Hankel determinant of certain univalent functions / J. Inequal. Appl. :281
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