FEKETE-SZEGO PROBLEM FOR CONCAVE UNIVALENT FUNCTIONS ASSOCIATED WITH FOX-WRIGHT'S GENERALIZED HYPERGEOMETRIC FUNCTIONS

Thomas Rosy, S. Sumil Varma, Gangadharan Murugusundaramoorthy

DOI Number
-
First page
465
Last page
477

Abstract


We investigate the Fekete-Szego problem with real and complex parameter $\lambda$ for the class Co(\lambda) of concave univalent functions dened by Fox-Wright's generalisedhypergeometric function.Mathematics Subject Classication: Primary 30C45Keywords: Concave, Univalent, Starlike functions, Fox-Wright's generalised hypergeometricfunction

Keywords


Concave, Univalent, Starlike functions, Fox-Wright's generalised hypergeometricfunction

Full Text:

PDF

References


References

Avkhadiev, F. G,and Wirths, K - J.Wirths, Concave schlict functions with bounded opening

angle at innity, Lobachevskii J. Math. (17), (2005), 3-10.

Avkhadiev, F. G, Pommerenke, C. H and Wirths, K - J.Wirths, Sharp inequalities for the

coecients of concave schlict functions, Comment. Math.Hele. (81), (2006), 801-807.

Bhowmik, B, Ponnusamy, S and K - J.Wirths, Characterization and the pre-Schwarzian

norm estimate for concave univalent functions, Monatschfte f ur Mathematik, online rst

DOI 10.007ns00605-009-0146-7, (2009).

Bhowmik, B, Ponnusamy, S and K - J.Wirths, On the Fekete-Szego problem for concave

univalent functions, Journal of Math. Analysis and appl. (373), (2011), 432-448.

S. D. Bernardi, Convex and starlike univalent functions, Trans. Amer. Math. Soc., 135

(1969), 429{446.

B. C. Carlson and S. B. Shaer, Starlike and prestarlike hypergeometric functions, SIAM

J. Math. Anal., 15 (1984), 737{745.

Choi, J. H, Kim, Y. C, Sugawa, T,A general approach to Fekete-Szeg _ o problem,

J.Math.Soc.Japan (59), No. (3), (2007), 707-727.

J. Dziok and H. M. Srivastava, Certain subclasses of analytic functions associated with the

generalized hypergeometric function, Intergral Transform Spec. Funct., 14 (2003), 7{18.

Duren, P.L., Univalent functions, Springer Verlag, New York. Inc. (1983).

Fekete, M. Szeg _ o, G, Eine Bemerkung uber ungerade schlict Funktionen, J.London Math

Soc.8, (1933), 85-89

Gangadharan Murugusundaramoorthy, Thomas Rosy, Subclasses of analytic functions

associated with Fox-Wright's generalised hypergeometric functions based on Hilbert space

operator, Stud. Univ. Babes-Bolyai Math. (56), No. (3), (2011), 61-72.

Koepf, W,On the Fekete-Szego problem for close-to-convex functions, Proc. Amer. Math.

Soc. (101), (1987), 420-433.

P

uger, A,The Fekete-Szego inequality for complex parameter, Complex Variables Theory

Appl. (7), (1986), n0. 1-3, 149-160.

R. J. Libera, Some classes of regular univalent functions, Proc. Amer. Math. Soc., 16

(1965), 755{758.

A. E. Livingston, On the radius of univalence of certain analytic functions, Proc. Amer.

Math. Soc., 17 (1966), 352{357.

H. M. Srivastava, Some Fox's-Wright generalized hypergeometric functions and associated

families of convolution operators, Applicable Analysis and Discrete Mathematics, 1 (2007),

-71.

E.M.Wright, The asymptotic expansion of the generalized hypergeometric function,Proc.

London. Math. Soc., 46 (1946), 389-408.


Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)