Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the second Hankel determinant of areally mean $ p$-valent functions


Authors: J. W. Noonan and D. K. Thomas
Journal: Trans. Amer. Math. Soc. 223 (1976), 337-346
MSC: Primary 30A36
DOI: https://doi.org/10.1090/S0002-9947-1976-0422607-9
MathSciNet review: 0422607
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we determine the growth rate of the second Hankel determinant of an areally mean p-valent function. This result both extends and unifies previously known results concerning this problem.


References [Enhancements On Off] (What's this?)

  • [1] W. K. Hayman, Multivalent functions, Cambridge Tracts in Math. and Math. Phys., no. 48, Cambridge Univ. Press, Cambridge, 1958. MR 21 #7302. MR 0108586 (21:7302)
  • [2] -, Research problems in function theory, Athlone Press, London, 1967. MR 36 #359. MR 0217268 (36:359)
  • [3] -, On successive coefficients of univalent functions, J. London Math. Soc. 38 (1963), 228-243. MR 26 #6382. MR 0148885 (26:6382)
  • [4] -, On the second Hankel determinant of mean univalent functions, Proc. London Math. Soc. (3) 18 (1968), 77-94. MR 36 #2794. MR 0219715 (36:2794)
  • [5] K. W. Lucas, A two-point modulus bound for areally mean p-valent functions, J. London Math. Soc. 43 (1968), 487-494. MR 37 #1587. MR 0225997 (37:1587)
  • [6] -, On successive coefficients of areally mean p-valent functions, J. London Math. Soc. 44 (1969), 631-642. MR 39 #4379. MR 0243055 (39:4379)
  • [7] J. W. Noonan, Coefficient differences and Hankel determinants of areally mean p-valent functions, Proc. Amer. Math. Soc. 46 (1974), 29-37. MR 0352440 (50:4927)
  • [8] J. W. Noonan and D. K. Thomas, On the Hankel determinants of areally mean p-valent functions, Proc. London Math. Soc. (3) 25 (1972), 503-524. MR 46 #5605. MR 0306479 (46:5605)
  • [9] Ch. Pommerenke, On the coefficients and Hankel determinants of univalent functions, J. London Math. Soc. 41 (1966), 111-122. MR 32 #2575. MR 0185105 (32:2575)
  • [10] -, On the Hankel determinants of univalent functions, Mathematika 14 (1967), 108-112. MR 35 #6811. MR 0215976 (35:6811)
  • [11] -, Über die Mittelwerte und Koeffizienten multivalenter Funktionen, Math. Ann. 145 (1961/62), 285-296. MR 24 #A3282. MR 0133448 (24:A3282)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 30A36

Retrieve articles in all journals with MSC: 30A36


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1976-0422607-9
Article copyright: © Copyright 1976 American Mathematical Society

American Mathematical Society