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On successive coefficients of close-to-convex functions

Published online by Cambridge University Press:  14 November 2011

M. M. Elhosh
M. M. Elhosh
Affiliation:
Department of Pure Mathematics, University College of Wales, Penglais, Aberystwyth SY23 3BZ
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Synopsis

A coefficient difference bound for k-fold symmetric and close-to-convex functions in the unit disc is established in this paper.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 96 , Issue 1-2 , 1984 , pp. 47 - 49
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

1Anderson, J. M., Barth, K. F. and Brannan, D. A.. Research problems in complex analysis. Bull. London Math. Soc. 9 (1977), 129–162.CrossRefGoogle Scholar
2Brannan, D. A. and Clunie, J. G.. Aspects of Contemporary Complex Analysis (London: Academic Press, 1980).Google Scholar
3Duren, P. L.. Coefficients of univalent functions. Bull. Amer. Math. Soc. 83 (1977), 891–911.CrossRefGoogle Scholar
4Duren, P. L.. Successive coefficients of univalent functions. J. London Math. Soc. 19 (1979), 448–450.Google Scholar
5Golusin, G. M.. Geometric theory of functions of a complex variable (Moscow: Gil TL, 1952); English transl., Transl. Math. Monographs Vol. 26 (Providence, R.I.: Amer. Math. Soc, 1969).Google Scholar
6Hayman, W. K.. Coefficient problems for univalent functions and related function classes. J. London Math. Soc. 40 (1965), 385–406.CrossRefGoogle Scholar
7Hayman, W. K.. On successive coefficients of univalent functions. J. London Math. Soc. 38 (1963), 228–243.CrossRefGoogle Scholar
8Hayman, W. K.. Research problems in function theory (London: Athlone Press, 1967).Google Scholar
9Kaplan, W. K.. Close-to-convex Schlicht functions. Michigan Math. J. 1 (1952), 169–185.CrossRefGoogle Scholar
10Leung, Yuk. Successive coefficients of starlike functions. Bull. London Math. Soc. 10 (1978), 193–196.Google Scholar
11Leung, Yuk. Robertson's conjecture on the coefficients of close-to-convex functions. Proc. Amer. Math. Soc. 76 (1-2), (1979), 89–94.Google Scholar
12Levin, V. I.. Ein Beitrag zum Koeffizientenproblem der Schlichten Funktionen. Math. Z. 38 (1933), 306–311.CrossRefGoogle Scholar
13Lucas, K. W.. On successive coefficients of areally mean p-valent functions. J. Ijondon Math. Soc. 44(1969), 631–642.CrossRefGoogle Scholar
14Keogh, F. R. and Miller, S. S.. On the coefficients of Bazilevic functions. Proc. Amer. Math. Soc. 30 (3) (1971), 492–496.Google Scholar
15Noonan, J. W.. On close-to-convex functions of order β. Pacific J. Math. 44 (1973), 263–280.CrossRefGoogle Scholar
16Pommerenke, Ch.. On starlike and close-to-convex functions. Proc. London Math. Soc. 13 (1963), 290–304.CrossRefGoogle Scholar
17Pommerenke, Ch.. On the coefficients of close-to-convex functions. Michigan Math. J. 9 (1962), 259–269.CrossRefGoogle Scholar
18Pommerenke, Ch.. Über die Mittelwerte und Koeffizienten multivalenter Funktionen. Math. Ann. 145 (1962), 285–296.CrossRefGoogle Scholar