Fekete-Szegő inequalities for close-to-convex functions

London, R. R.

doi:10.1090/S0002-9939-1993-1150652-2

Fekete-Szegő inequalities for close-to-convex functions
HTML articles powered by AMS MathViewer

by R. R. London PDF

Proc. Amer. Math. Soc. 117 (1993), 947-950 Request permission

Abstract:

Let $K(\beta )$ denote the class of normalised close-to-convex functions of order $\beta$ defined in the unit disc, and let $f \in K(\beta )$ with $f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \cdots$. Sharp bounds are obtained for $|{a_3} - \mu a_2^2|$, where $\mu$ is real.

References

Eine Bermerkung über ungerade schlichte Funktionen

8

H. R. Abdel-Gawad and D. K. Thomas, The Fekete-Szegő problem for strongly close-to-convex functions, Proc. Amer. Math. Soc. 114 (1992), no. 2, 345–349. MR 1065939, DOI 10.1090/S0002-9939-1992-1065939-0
F. R. Keogh and E. P. Merkes, A coefficient inequality for certain classes of analytic functions, Proc. Amer. Math. Soc. 20 (1969), 8–12. MR 232926, DOI 10.1090/S0002-9939-1969-0232926-9
Wolfram Koepf, On the Fekete-Szegő problem for close-to-convex functions, Proc. Amer. Math. Soc. 101 (1987), no. 1, 89–95. MR 897076, DOI 10.1090/S0002-9939-1987-0897076-8
Wolfram Koepf, On the Fekete-Szegő problem for close-to-convex functions. II, Arch. Math. (Basel) 49 (1987), no. 5, 420–433. MR 915916, DOI 10.1007/BF01194100
Albert Pfluger, The Fekete-Szegő inequality for complex parameters, Complex Variables Theory Appl. 7 (1986), no. 1-3, 149–160. MR 877660, DOI 10.1080/17476938608814195
Ch. Pommerenke, On close-to-convex analytic functions, Trans. Amer. Math. Soc. 114 (1965), 176–186. MR 174720, DOI 10.1090/S0002-9947-1965-0174720-4
Christian Pommerenke, Univalent functions, Studia Mathematica/Mathematische Lehrbücher, Band XXV, Vandenhoeck & Ruprecht, Göttingen, 1975. With a chapter on quadratic differentials by Gerd Jensen. MR 0507768