Close-to-convex multivalent functions with respect to weakly starlike functions
HTML articles powered by AMS MathViewer
- by David Styer PDF
- Trans. Amer. Math. Soc. 169 (1972), 105-112 Request permission
Abstract:
It is the object of this article to define close-to-convex multivalent functions in terms of weakly starlike multivalent functions. Six classes are defined, and shown to be equal. These generalize the class of close-to-convex functions developed by Livingston in the article, $p$-valent close-to-convex functions, Trans. Amer. Math. Soc. 115 (1965), 161-179.References
- J. A. Hummel, Multivalent starlike functions, J. Analyse Math. 18 (1967), 133–160. MR 209461, DOI 10.1007/BF02798041
- Wilfred Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169–185 (1953). MR 54711
- 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
- David Styer, On weakly starlike multivalent functions, J. Analyse Math. 26 (1973), 217–233. MR 328053, DOI 10.1007/BF02790430
- Toshio Umezawa, On the theory of univalent functions, Tohoku Math. J. (2) 7 (1955), 212–228. MR 77630, DOI 10.2748/tmj/1178245060 H. S. Wall, Analytic theory of continued fractions, Chelsea, New York, 1967.
Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 169 (1972), 105-112
- MSC: Primary 30A36; Secondary 30A32
- DOI: https://doi.org/10.1090/S0002-9947-1972-0315117-7
- MathSciNet review: 0315117