On a class of analytic multivalent functions

Abstract We use a property of the Bernardi operator in the theory of the Briot–Bouquet differential subordinations to prove several theorems for the classes V k p ( H ; A , B ) of multivalent analytic functions defined by using the Dziok–Srivastava operator H . Some of these results we obtain applying the convolution property due to Rusheweyh. We take advantage of the Miller–Mocanu lemma to improve the earlier result.

[1]  Hari M. Srivastava,et al.  Current topics in analytic function theory , 1992 .

[2]  S. D. Bernardi,et al.  THE RADIUS OF UNIVALENCE OF CERTAIN ANALYTIC FUNCTIONS , 1966 .

[3]  T. Sheil-Small,et al.  Hadamard products of Schlicht functions and the Pólya-Schoenberg conjecture , 1973 .

[4]  Sanford S. Miller,et al.  Differential Subordinations: Theory and Applications , 2000 .

[5]  Hari M. Srivastava,et al.  Some inclusion properties of a certain family of integral operators , 2002 .

[6]  E. Kirjackis,et al.  Classes of analytic functions , 1985 .

[7]  W. Janowski,et al.  Extremal problems for a family of functions with positive real part and for some related families , 1970 .

[8]  Stephan Ruscheweyh NEW CRITERIA FOR UNIVALENT FUNCTIONS , 1975 .

[9]  Toshio Umezawa,et al.  ON THE THEORY OF UNIVALENT FUNCTIONS , 1955 .

[10]  Hari M. Srivastava,et al.  A certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients , 1992 .

[11]  Hari M. Srivastava,et al.  Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions , 1987, Nagoya Mathematical Journal.

[12]  B. C. Carlson,et al.  Starlike and Prestarlike Hypergeometric Functions , 1984 .

[13]  Stephan Ruscheweyh,et al.  Convolutions in Geometric Function Theory , 1982 .

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

[15]  Hari M. Srivastava,et al.  Fractional integral and other linear operators associated with the gaussian hypergeometric function , 1997 .

[16]  S. D. Bernardi,et al.  Convex and starlike univalent functions , 1969 .

[17]  R. J. Libera Some classes of regular univalent functions , 1965 .

[18]  Yong Chan Kim,et al.  Some applications of a differential subordination , 1999 .

[19]  Hassoon S. Al-Amiri,et al.  On the radius of univalence of certain analytic functions , 1973 .