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On the logarithmic coefficients of close-to-convex functions

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

M. M. Elhosh
M. M. Elhosh
Affiliation:
Department of MathematicsThe University College of WalesAberystwythDyfed, UK
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Abstract

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Logarithmic coefficient bounds for some univalent functions are given in this paper.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 30C50: Coefficient problems for univalent and multivalent functions 30C55: General theory of univalent and multivalent functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 1 , February 1996 , pp. 1 - 6
Copyright
Copyright © Australian Mathematical Society 1996

References

[1]Anderson, J., Barth, K. and Brannan, D., ‘Research problems in complex analysis’, Bull. London Math. Soc. 9 (1977), 129–162.Google Scholar
[2]de Branges, L., ‘A proof of the Bieberbach Conjecture’, Acta Math. 154 (1985), 137–152.Google Scholar
[3]Brannan, D. and Clunie, J., Aspects of contemporary complex analysis (Academic Press, 1980).Google Scholar
[4]Brickman, L., Hallenbeck, D. and MacGregor, T., ‘Convex hulls and extreme points of families of starlike and convex mappings’, Trans. Amer. Math. Soc. 185 (1973), 413–428.Google Scholar
[5]Duren, P., ‘Coefficients of univalent functions’, Bull. Amer. Math. Soc. (5) 83 (1977), 891–911.CrossRefGoogle Scholar
[6]Duren, P., Univalent functions (Springer, New York, 1983).Google Scholar
[7]Duren, P. and Leung, Y., ‘Logarithmic coefficients of univalent functions’, J. Analyse Math. 36 (1979), 36–43.CrossRefGoogle Scholar
[8]Elhosh, M. M., ‘On the logarithmic coefficients of close-to-convex functions’, Math. Japon. (2) 31 (1986), 201–204.Google Scholar
[9]Elhosh, M. M., ‘On mean p-valent functions’, Rev. Roumanie Math. Pures Appl. 34 (1989), 11–15.Google Scholar
[10]Girela, D., ‘Integral means and BMOA norms of logarithms of univalent functions’, J. London Math. Soc. 33 (1986), 117–132.CrossRefGoogle Scholar
[11]Hallenbeck, D. and MacGregor, T., Linear problems and convexity techniques in geometric function theory (Pitman, London, 1984).Google Scholar
[12]Hille, E., Ordinary differential equations in the complex domain (Wiley, New York, 1976).Google Scholar
[13]Koepf, W., ‘On the Fekete-Szego problem for close-to-convex functions’, Proc. Amer. Math. Soc. 101 (1987), 89–95.Google Scholar
[14]MacGregor, T., ‘Applications of extreme point theory to univalent functions’, Michigan Math. J. 19 (1972), 361–376.CrossRefGoogle Scholar
[15]Pearce, K., ‘New support points of S and extreme points of KS’, Proc. Amer. Math. Soc. 81 (1981), 425–428.Google Scholar
[16]Pinchuk, B., ‘On starlike and convex functions of order α’, Duke Math. J. 35 (1968), 721–734.Google Scholar
[17]Robinson, R., ‘On the theory of univalent functions’, Ann. of Math. 37 (1936), 1–35.Google Scholar