On some classes of multivalent starlike functions

Leach, Ronald J.

doi:10.1090/S0002-9947-1975-0369677-3

On some classes of multivalent starlike functions
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by Ronald J. Leach

Trans. Amer. Math. Soc. 209 (1975), 267-273

DOI: https://doi.org/10.1090/S0002-9947-1975-0369677-3

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Abstract:

Classes of multivalent functions analogous to certain classes of univalent starlike functions are defined and studied. Estimates on coefficients and distortion are made, using a variety of techniques.

References

D. A. Brannan, J. Clunie, and W. E. Kirwan, Coefficient estimates for a class of star-like functions, Canadian J. Math. 22 (1970), 476–485. MR 260994, DOI 10.4153/CJM-1970-055-8
D. A. Brannan and W. E. Kirwan, On some classes of bounded univalent functions, J. London Math. Soc. (2) 1 (1969), 431–443. MR 251208, DOI 10.1112/jlms/s2-1.1.431
L. Brickman, D. J. Hallenbeck, T. H. MacGregor, and D. R. Wilken, Convex hulls and extreme points of families of starlike and convex mappings, Trans. Amer. Math. Soc. 185 (1973), 413–428 (1974). MR 338337, DOI 10.1090/S0002-9947-1973-0338337-5
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
J. A. Hummel, Multivalent starlike functions, J. Analyse Math. 18 (1967), 133–160. MR 209461, DOI 10.1007/BF02798041
James A. Hummel, Extremal properties of weakly starlike $p$-valent functions, Trans. Amer. Math. Soc. 130 (1968), 544–551. MR 222280, DOI 10.1090/S0002-9947-1968-0222280-4
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
P. K. Kulshrestha, Coefficients for alpha-convex univalent functions, Bull. Amer. Math. Soc. 80 (1974), 341–342. MR 342689, DOI 10.1090/S0002-9904-1974-13494-4
Sanford S. Miller, Distortions properties of alpha-starlike functions, Proc. Amer. Math. Soc. 38 (1973), 311–318. MR 310222, DOI 10.1090/S0002-9939-1973-0310222-X
Petru T. Mocanu, Une propriété de convexité généralisée dans la théorie de la représentation conforme, Mathematica (Cluj) 11(34) (1969), 127–133 (French). MR 273000
Malcolm I. S. Robertson, On the theory of univalent functions, Ann. of Math. (2) 37 (1936), no. 2, 374–408. MR 1503286, DOI 10.2307/1968451
J. Szynal, Some remarks on coefficients inequality for $a$-convex functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. Astronom. Phys. 20 (1972), 917–919 (English, with Russian summary). MR 311892