On certain subclasses of analytic functions defined by wright generalized hypergeometric functions

2009 ◽  
Vol 30 (1) ◽  
pp. 57-66
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Wright Generalized Hypergeometric Functions

New subclasses of analytic functions defined by convolution involving the hypergeometric function and the Owa–Srivastava operator

2019 ◽  
Vol 26 (3) ◽  
pp. 449-458
Author(s):  
Khalida Inayat Noor ◽  
Rashid Murtaza ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Convolution Operator ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Integral Operators ◽  
Generalized Hypergeometric Functions ◽  
Convolution Properties ◽  
Appl Math ◽  
Inclusion Results

Abstract In the present paper we introduce a new convolution operator on the class of all normalized analytic functions in {|z|<1} , by using the hypergeometric function and the Owa–Srivastava operator {\Omega^{\alpha}} defined in [S. Owa and H. M. Srivastava, Univalent and starlike generalized hypergeometric functions, Canad. J. Math. 39 1987, 5, 1057–1077]. This operator is a generalization of the operators defined in [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365] and [K. I. Noor, Integral operators defined by convolution with hypergeometric functions, Appl. Math. Comput. 182 2006, 2, 1872–1881]. Also we introduce some new subclasses of analytic functions using this operator and we discuss some interesting results, such as inclusion results and convolution properties. Our results generalize the results of [S. K. Lee and K. M. Khairnar, A new subclass of analytic functions defined by convolution, Korean J. Math. 19 2011, 4, 351–365].

scholarly journals Some characterization and distortion theorems involving fractional calculus, generalized hypergeometric functions, Hadamard products, linear operators, and certain subclasses of analytic functions

1987 ◽  
Vol 106 ◽  
pp. 1-28 ◽  
Author(s):  
H. M. Srivastava ◽  
Shigeyoshi Owa
Keyword(s):  
Fractional Calculus ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Linear Operators ◽  
Coefficient Estimates ◽  
Hadamard Products ◽  
Generalized Hypergeometric Functions ◽  
Hypergeometric Type ◽  
Distortion Theorems ◽  
Characterization Theorems

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disk are introduced and studied systematically. The various results presented here include, for example, a number of coefficient estimates and distortion theorems for functions belonging to these subclasses, some interesting relationships between these subclasses, and a wide variety of characterization theorems involving a certain functional, some general functions of hypergeometric type, and operators of fractional calculus. Some of the coefficient estimates obtained here are fruitfully applied in the investigation of certain subclasses of analytic functions with fixed finitely many coefficients.

scholarly journals Subclasses of Analytic Functions Defined by Generalized Hypergeometric Functions

2016 ◽  
Vol 2016 ◽  
pp. 1-6 ◽  
Author(s):  
Badr S. Alkahtani ◽  
Saima Mustafa ◽  
Teodor Bulboacă
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Generalized Hypergeometric Functions ◽  
Radius Problems ◽  
Inclusion Results

We introduce a new subclass of analytic functions in the unit diskU, defined by using the generalized hypergeometric functions, which extends some previous well-known classes defined by different authors. Inclusion results, radius problems, and some connections with the Bernardi-Libera-Livingston integral operator are discussed.

Multi-parametric mittag-leffler functions and their extension

2013 ◽  
Vol 16 (2) ◽  
Author(s):  
Anatoly Kilbas ◽  
Anna Koroleva ◽  
Sergei Rogosin
Keyword(s):  
Fractional Calculus ◽  
Historical Development ◽  
Hypergeometric Functions ◽  
Special Functions ◽  
Integral Representations ◽  
Generalized Hypergeometric Functions ◽  
Late Professor ◽  
Wright Generalized Hypergeometric Functions

AbstractThis paper surveys one of the last contributions by the late Professor Anatoly Kilbas (1948–2010) and research made under his advisorship. We briefly describe the historical development of the theory of the discussed multi-parametric Mittag-Leffler functions as a class of the Wright generalized hypergeometric functions. The method of the Mellin-Barnes integral representations allows us to extend the considered functions to the case of arbitrary values of parameters. Thus, the extended Mittag-Leffler-type functions appear. The properties of these special functions and their relations to the fractional calculus are considered. Our results are based mainly on the properties of the Fox H-functions, as one of the widest class of special functions.

scholarly journals Subclass of Multivalent Harmonic Functions Defi…ned by Wright Generalized Hypergeometric Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
M. K. Aouf ◽  
A. O. Moustafa ◽  
E. A. Adwan
Keyword(s):  
Harmonic Functions ◽  
Hypergeometric Functions ◽  
Convex Combination ◽  
Extreme Points ◽  
Coefficient Estimates ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Function Coefficient ◽  
Distortion Bounds ◽  
Wright Generalized Hypergeometric Functions

We introduce a new class of multivalent harmonic functions defi…ned by Wright generalized hypergeometric function. Coefficient estimates, extreme points, distortion bounds, and convex combination for functions belonging to this class are obtained.

Sign in / Sign up

Export Citation Format

Share Document