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Proceedings of the American Mathematical Society

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Spirallike nonanalytic functions


Authors: Hassoon Al-Amiri and Petru T. Mocanu
Journal: Proc. Amer. Math. Soc. 82 (1981), 61-65
MSC: Primary 30C99; Secondary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1981-0603602-0
MathSciNet review: 603602
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Abstract: Let $ f(z) = u(x,y) + i\upsilon (x,y)$ be a complex function defined in the unit disc $ U.f$ is said to belong to the class $ {C^1}(U)$ if the functions $ u(x,y)$ and $ \upsilon (x,y)$ have continuous first order partial derivatives in $ U$. We determine sufficient conditions for functions in the class $ {C^1}(U)$ to be univalent and to map $ U$ onto spirallike domains. These conditions are similar to those in the analytic case as given by Spaček and Rakhmanov.


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

  • [1] Petru T. Mocanu, Starlikeness and convexity for nonanalytic functions in the unit disc, Mathematica (Cluj) 22(45) (1980), no. 1, 77–83. MR 618032
  • [2] B. N. Rahmanov, On the theory of univalent functions, Doklady Akad. Nauk SSSR (N.S.) 91 (1953), 729–732 (Russian). MR 0058711
  • [3] -, On the theory of schlicht functions, Dokl. Akad. Nauk SSSR 97 (1954), 973-976. (Russian)
  • [4] L. Spaček, Contribution à la théorie des fonctions univalentes, Časopis Pěst. Mat. 62 (1933), 12-19.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0603602-0
Keywords: Univalent, starlike, spirallike, Jacobian, nonanalytic functions
Article copyright: © Copyright 1981 American Mathematical Society