Inclusion results for certain subclasses of spiral-like multivalent functions involving a generalized fractional differintegral operator

Let Ap denote the class of analytic and p-valent functions in the open unit disc U={z:|z|<1}. Put and define in terms of the Hadmard product (or convolution) In this paper, we introduce certain new subclasses of spiral-like multivalent functions defined by using the operator and investigate several inclusion properties of these classes. Also, some applications involving integral operator are considered.

[1]  M. K. Aouf,et al.  Some properties of Noor integral operator of -th order. , 2009 .

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

[3]  Hari M. Srivastava,et al.  Univalent and Starlike Generalized Hypergeometric Functions , 1987, Canadian Journal of Mathematics.

[4]  Mohamed Kamal Aouf,et al.  Majorization problem for certain class of p-valently analytic function defined by generalized fractional differintegral operator , 2012, Comput. Math. Appl..

[5]  Jin-Lin Liu,et al.  The Noor Integral and Strongly Starlike Functions , 2001 .

[6]  W. K. Hayman.  UNIVALENT FUNCTIONS (Grundlehren der mathematischen Wissenschaften, 259) , 1984 .

[7]  Hari M. Srivastava,et al.  Some inclusion properties for certain subclasses of strongly starlike and strongly convex functions involving a family of fractional integral operators , 2007 .

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

[9]  Hari M. Srivastava,et al.  A class of distortion theorems involving certain operators of fractional calculus , 1988 .

[10]  M. Hasse,et al.  W. H. Greub, Multilinear Algebra. (Die Grundlehren der mathematischen Wissenschaften. Band 136). XII + 225 S. Berlin/Heidelberg/New York 1967. Springer-Verlag. Preis geb. DM 32,– , 1971 .

[11]  Sanford S. Miller,et al.  Differential subordinations and univalent functions. , 1981 .

[12]  S. P. Goyal,et al.  A New Class of Analytic p-Valent Functions with Negative Coefficients and Fractional Calculus Operators , 2004 .

[13]  Hari M. Srivastava,et al.  Some applications of the generalized Libera integral operator , 1986 .

[14]  Hari M. Srivastava,et al.  Inclusion properties of a subclass of analytic functions defined by an integral operator involving the Gauss hypergeometric function , 2011, Appl. Math. Comput..

[15]  Nak Eun Cho,et al.  Inclusion properties of certain subclasses of analytic functions defined by a multiplier transformation , 2006, Comput. Math. Appl..

[16]  Sanford S. Miller,et al.  On a Briot-Bouquet Differential Subordination , 1983 .

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

[18]  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.