A coefficient estimate for multivalent functions
HTML articles powered by AMS MathViewer
- by David J. Hallenbeck and Albert E. Livingston PDF
- Proc. Amer. Math. Soc. 54 (1976), 201-206 Request permission
Abstract:
By making use of extreme point theory we obtain bounds on the coefficients of a class of functions, multivalent in the unit disk, closely related to the bounds conjectured by Goodman.References
- A. W. Goodman, On some determinants related to $p$-valent functions, Trans. Amer. Math. Soc. 63 (1948), 175–192. MR 23910, DOI 10.1090/S0002-9947-1948-0023910-X
- A. W. Goodman, On the Schwarz-Christoffel transformation and $p$-valent functions, Trans. Amer. Math. Soc. 68 (1950), 204–223. MR 33886, DOI 10.1090/S0002-9947-1950-0033886-6
- A. W. Goodman and M. S. Robertson, A class of multivalent functions, Trans. Amer. Math. Soc. 70 (1951), 127–136. MR 40430, DOI 10.1090/S0002-9947-1951-0040430-7
- David J. Hallenbeck and Albert E. Livingston, Applications of extreme point theory to classes of multivalent functions, Trans. Amer. Math. Soc. 221 (1976), no. 2, 339–359. MR 407257, DOI 10.1090/S0002-9947-1976-0407257-2
- A. E. Livingston, $p$-valent close-to-convex functions, Trans. Amer. Math. Soc. 115 (1965), 161–179. MR 199373, DOI 10.1090/S0002-9947-1965-0199373-0
- Albert E. Livingston, The coefficients of multivalent close-to-convex functions, Proc. Amer. Math. Soc. 21 (1969), 545–552. MR 243054, DOI 10.1090/S0002-9939-1969-0243054-0
- M. S. Robertson, A coefficient problem for functions regular in an annulus, Canad. J. Math. 4 (1952), 407–423. MR 51308, DOI 10.4153/cjm-1952-037-1
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 54 (1976), 201-206
- DOI: https://doi.org/10.1090/S0002-9939-1976-0387561-2
- MathSciNet review: 0387561