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In this paper we obtain the bounds of the third Hankel determinants for the classes $\mathcal{S}^\ast(\alpha)$ of starlike functions of order $\alpha$ and $\mathcal{K}(\alpha)$ of convex functions of order $\alpha$. Moreover,we derive the sharp bounds for functions in these classes which are additionally 2-fold or 3-fold symmetric.
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참고문헌 (21)
참고문헌 신청
Y. Abu Muhanna / 2014 / Extremal problems on the class of convex functions of order -1/2 / Arch. Math. 103(6):461~471
K. O. Babalola / 2010 / On $H_3$ (1) Hankel determinants for some classes of univalent functions;Inequality Theory and Applications, Vol. 6 / Nova Science Publishers :1~7
Deepak Bansal / 2015 / THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS / 대한수학회지 52(6):1139~1148
D. Bshouty / 2011 / Close-to-convexity criteria for planar harmonic mappings / Complex Anal. Oper. Theory 5(3):767~774
R. F. Gabriel / 1955 / The Schwarzian derivative and convex functions / Proc. Amer. Math. Soc. 6:58~66
K. O. Babalola / 2010 / On
Deepak Bansal / 2015 / THIRD ORDER HANKEL DETERMINANT FOR CERTAIN UNIVALENT FUNCTIONS / 대한수학회지 52(6):1139~1148
D. Bshouty / 2011 / Close-to-convexity criteria for planar harmonic mappings / Complex Anal. Oper. Theory 5(3):767~774
R. F. Gabriel / 1955 / The Schwarzian derivative and convex functions / Proc. Amer. Math. Soc. 6:58~66
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