JOURNAL BROWSE
Search
Advanced SearchSearch Tips
REGIONS OF VARIABILITY FOR GENERALIZED α-CONVEX AND β-STARLIKE FUNCTIONS, AND THEIR EXTREME POINTS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
REGIONS OF VARIABILITY FOR GENERALIZED α-CONVEX AND β-STARLIKE FUNCTIONS, AND THEIR EXTREME POINTS
Chen, Shaolin; Huang, Aiwu;
  PDF(new window)
 Abstract
Suppose that n is a positive integer. For any real number ( resp.) with < 1 ( > 1 resp.), let ( resp.) be the class of analytic functions in the unit disk with f(0)
 Keywords
Schwarz lemma;analytic function;univalent function;starlike function;generalized -convex domain;-starlike function;region of variability;extreme point;
 Language
English
 Cited by
 References
1.
Y. Abu-Muhanna and T. H. MacGregor, Extreme points of families of analytic functions subordinate to convex mappings, Math. Z. 176 (1981), no. 4, 511–519. crossref(new window)

2.
P. L. Duren, Univalent Function, Grundlehren der mathematicchen Wissenschaften 259, New York, Berlin, Heidelberg, Tokyo, Spring-Verlag, 1983.

3.
A. W. Goodman, Univalent Functions, Vols. I and II, Mariner Publishing Co., Tampa, Florida, 1983.

4.
D. J. Hallenbeck, Extreme points of classes of functions defined by subordination, Proc. Amer. Math. Soc. 46 (1974), 59–64.

5.
D. J. Hallenbeck and A. E. Livingston, Applications of extreme point theory to classes of multivalent functions, Trans. Amer. Math. Soc. 221 (1976), no. 2, 339–359.

6.
Ch. Pommerenke, Boundary Behaviour of Conform Maps, Springer-Verlag, Berlin, 1992.

7.
S. Ponnusamy, Foundations of Functional Analysis, Alpha Science International Ltd., Pangbourne, 2002.

8.
S. Ponnusamy and H. Silverman, Complex Variables with Applications, Birkhauser, Boston, 2006.

9.
S. Ponnusamy and V. Singh, Univalence of certain integral transforms, Glas. Mat. Ser. III 31(51) (1996), no. 2, 253–261.

10.
S. Ponnusamy and A. Vasudevarao, Region of variability of two subclasses of univalent functions, J. Math. Anal. Appl. 332 (2007), no. 2, 1323–1334. crossref(new window)

11.
S. Ponnusamy, A. Vasudevarao, and H. Yanagihara, Region of variability of univalent functions f(z) for which zf'(z) is spirallike, Houston J. Math. 34 (2008), no. 4, 1037–1048.

12.
J. Vaisala, Uniform domains, Tohoku Math. J. (2) 40 (1988), no. 1, 101–118. crossref(new window)

13.
X. Wang, M. Huang, and Y. Chu, Bounded and convex domains in Rn, Acta Math. Sinica (Chin. Ser.) 50 (2007), no. 3, 481–484.

14.
H. Yanagihara, Regions of variability for functions of bounded derivatives, Kodai Math. J. 28 (2005), no. 2, 452–462.