Applications of extreme points to distortion estimates

The main object of this paper is to introduce and investigate a class of analytic functions with negative coefficients defined by the Wright generalized hypergeometric function. By using the extreme points theory we obtain coefficient estimates and distortion theorems in the class of functions.

[1]  Hari M. Srivastava,et al.  Certain properties of the Dziok-Srivastava operator , 2004, Appl. Math. Comput..

[2]  Hari M. Srivastava,et al.  The H-functions of one and two variables, with applications , 1982 .

[3]  R. K. Raina.  On univalent and starlike Wright's hypergeometric functions , 1996 .

[4]  Ravinder Krishna Raina,et al.  FAMILIES OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE WRIGHT GENERALIZED HYPERGEOMETRIC FUNCTION , 2004 .

[5]  Kellen Petersen August.  Real Analysis , 2009 .

[6]  Hari M. Srivastava,et al.  Certain Subclasses of Analytic Functions Associated with the Generalized Hypergeometric Function , 2003 .

[7]  Janusz Sokól.  On a class of analytic multivalent functions , 2008, Appl. Math. Comput..

[8]  Ravinder Krishna Raina,et al.  On Characterization of Certain Wright's Generalized Hypergeometric Functions Involving Certain Subclasses of Analytic Functions , 1999, Informatica.

[9]  V. Kiryakova.  Generalized Fractional Calculus and Applications , 1993 .

[10]  M. Kreĭn,et al.  On extreme points of regular convex sets , 1940 .

[11]  J. Dziok,et al.  On the convex combination of the Dziok-Srivastava operator , 2007, Appl. Math. Comput..

[12]  E. Wright.  The Asymptotic Expansion of the Generalized Hypergeometric Function , 1935 .

[13]  Janusz Sokól.  On some applications of the Dziok-Srivastava operator , 2008, Appl. Math. Comput..

[14]  P. W. Karlsson,et al.  Multiple Gaussian hypergeometric series , 1985 .

[15]  Hari M. Srivastava,et al.  Generalized hypergeometric functions associated with k-uniformly convex functions , 2002 .

[16]  Yu. A. Brychkov,et al.  Integrals and series , 1992 .

[17]  D. J. Hallenbeck,et al.  Linear problems and convexity techniques in geometric function theory , 1984 .

[18]  E. Verspohl.  The pharmacy and pharmacotherapy of asthma. Ed. by P. F. D'Arcy and J. C. McElnay. Ellis Horwood Series in Pharmaceutical Technology. Halsted Press: A division of John Wiley & Sons, New York/Chichester/Brisbane/Toronto. 258 S., zahlr. Abb., geb. £ 49.95 , 1990 .

[19]  Hari M. Srivastava,et al.  Classes of analytic functions associated with the generalized hypergeometric function , 1999, Appl. Math. Comput..