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K-Fold symmetric starlike univalent functions

Published online by Cambridge University Press:  17 April 2009

V. V. Anh
V. V. Anh
Affiliation:
Department of Mathematics, Queensland Institute of Technology, P.O. Box 2434, Brisbane, Q. 4001, Australia.
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Abstract

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This paper establishes the radius of convexity, distortion and covering theorems for the class

where

−1 ≤ B < A ≤ 1, w(0) = 0, |w (z)| < 1 in the unit disc. Coefficient bounds for functions in are also derived.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 32 , Issue 3 , December 1985 , pp. 419 - 436
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Anh, V. V. and Tuan, P. D., “On β-convexity of certain starlike univalent functions”, Rev. Roum. Math. Pures et Appl. 24 (1979), 1413–1424.Google Scholar
[2]Clunie, J., “On meromorphic Schlicht functions”, J. London Math. Soc. 34 (1959), 215–216.CrossRefGoogle Scholar
[3]Duren, P.L., Univalent functions, Springer Verlag, New York, 1983.Google Scholar
[4]Golusin, G.M., “On some estimates for functions which map the circle conformally and univalently”, Recueil Math. Moscow 36 (1929), 152–172.Google Scholar
[5]Janowski, W., “Extremal problems for a family of functions with positive real part and for some related families”, Ann. Polon. Math. 23 (1970), 159–177.CrossRefGoogle Scholar
[6]Janowski, W., “Some extremal problems for certain families of analytic functions I’ Ann. Polon. Math. 28 (1973), 298–326.CrossRefGoogle Scholar
[7]Libera, R.J., ‘Some radius of convexity problems”, Duke Math. J. 31 (1964), 143–158.CrossRefGoogle Scholar
[8]McCarty, C. P., ‘Startlike functions”, Proc. Amer. Math. Soc. 43 (1974), 361–366.CrossRefGoogle Scholar
[9]MacGregor, T.H., “Coefficient estimates for starlike mappings”, Michigon Math. J., 10 (1963), 277–281.Google Scholar
[10]Nehari, Z., Conformal Mappings, (McGraw-Hill, New York, 1952.)Google Scholar
[11]Noshiro, K., “On the theory of schlicht functions”, J. Fac. Sci Hokkaido Univ., Ser. I Math. 2 (1934), 129–155.Google Scholar
[12]Padmanabhan, K.S., “On certain classes of starlike functions in the unit disk”, J. Indian Math. Soc. 32 (1968), 89–103.Google Scholar
[13]Robertson, M.S., “On the theory of univalent functions”, Ann. of Math. 37 (1936), 374–408.CrossRefGoogle Scholar
[14]Robertson, M.S., “Variational methods for functions with positive real part”, Trans. Amer. Math. Soc. 101 (1962), 82–93.CrossRefGoogle Scholar
[15]Robertson, M.S., “Extremal problems for analytic functions with positive real part and applications”, Trans. Amer. Math. Soc. 106 (1963), 236–253.CrossRefGoogle Scholar
[16]Zawadzki, R., “On some theorems on distortion and rotation in the class of k-symmetrical starlike functions of order α”, Ann. Polon. Math. 24 (1971), 169–185.CrossRefGoogle Scholar
[17]Zawadzki, R., “On the radius of convexity of some class of analytic k-symmetrical functions”, Ann. Univ. Mariae Curie-Sklodowska, Sectio A, 26 (1972), 79–101.Google Scholar
[18]Zmorovic, V.A., “On bounds of convexity for starlike functions of order α in the circle |z| < 1 and in the circular region 0 < |z 1, Mat. Sb., 68 (1965), 518–526, English Transl., Amer. Math. Soc. Transl. (2), 80 (1969), 203–213.Google Scholar