Hostname: page-component-848d4c4894-nr4z6 Total loading time: 0 Render date: 2024-06-08T21:01:14.504Z Has data issue: false hasContentIssue false
  • English
  • Français

Disproof of a coefficient estimate related to Bazilevic functions

Published online by Cambridge University Press:  17 April 2009

Massoud Jahangiri
Massoud Jahangiri
Affiliation:
Department of Mathematics, University of California Davis, CA 95616, United States of America
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A coefficient estimate for powers of a class of Bazilevic functions obtained by M.M. Elhosh, is disproved and some sharp bounds are given.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 42 , Issue 1 , August 1990 , pp. 121 - 124
Copyright
Copyright © Australian Mathematical Society 1990

References

[1]Bazilevic, I.E., ‘On a case of integrability by quadratures of the Loewner-Kufarev equation’, Math. Sb. N.S. 37 (79) (1955), 471–476. (Russian).Google Scholar
[2]Bernardi, S.D., Bibliography of Schlicht functions (Mariner Pub. Co., Tampa, Florida, 1982).Google Scholar
[3]Eenigenburg, P.J. and Silvia, E.M., ‘A coefficient inequality for Bazilevic functions’, (Polish and Russian summaries), Ann. Univ. Marine Curie-Sklodowska Sect. A 27 (1973), 5–12.Google Scholar
[4]Elhosh, M.M., ‘On a subclass of Bazilevic functions’, Bull. Austral. Math. Soc. 39 (1989), 167–170.CrossRefGoogle Scholar
[5]Goodman, A.W., Univalent functions Vol. I (Mariner Pub. Co., Tampa, Florida, 1983).Google Scholar
[6]Hayman, W.K. and Hummel, J.A., ‘Coefficients of powers of univalent functions’, Complex Variables 7 (1986), 51–70.Google Scholar
[7]Jahangiri, M., ‘On the coefficients of powers of a class of Bazilevic functions’, Indian J. Pure Appl. Math. 17 (9) (1986), 1140–1144.Google Scholar
[8]Leach, R.J., ‘The coefficient problem for Bazilevic functions’, Houston J. Math. 4 (6) (1980), 543–547.Google Scholar
[9]Mocanu, P.T., ‘Une Propriete de convexite generalisee dans la theorie de la representation conforme’, Mathematics 11 (34) (1969), 127–133.Google Scholar
[10]Szynal, J., ‘Some remarks on coefficients inequality for α-convex functions’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 20 (1972), 917–920.Google Scholar
[11]Szynal, J. and Wajler, S., ‘On the fourth coefficient for α-convex functions’, Rev. Roumaine Math. Pures Appl. 19 (1974), 1153–1157.Google Scholar