scholarly journals Some results on certain subclasses of analytic functions involving generalized hypergeometric functions and Hadamard product

1992 ◽  
Vol 15 (1) ◽  
pp. 143-148
Author(s):  
Khalida Inayat Noor
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
Generalized Hypergeometric Functions ◽  
Hypergeometric Type

By using a certain linear operator defined by a Hadamard product or convolution, several interesting subclasses of analytic functions in the unit disc are introduced and some unifying relationships between them are established. A variety of characterization results involving a certain functional and some general functions of hypergeometric type are investigated for these classes.

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 Some classes of p-valent analytic functions associated with hypergeometric functions

Filomat ◽  
2015 ◽  
Vol 29 (5) ◽  
pp. 1031-1038 ◽  
Author(s):  
Khalida Noor ◽  
Nasir Khan
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Class A ◽  
Radius Problem ◽  
Inclusion Results

We define a linear operator on the class A(p) of p-valent analytic functions in the open unit disc involving Gauss hypergeometric functions and introduce certain new subclasses of A(p) using this operator. Some inclusion results, a radius problem and several other interesting properties of these classes are studied.

scholarly journals A New Class of Meromorphically Analytic Functions with Applications to the Generalized Hypergeometric Functions

2011 ◽  
Vol 2011 ◽  
pp. 1-10 ◽  
Author(s):  
Firas Ghanim ◽  
Maslina Darus
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
The Other ◽  
Radius Of Starlikeness ◽  
Generalized Hypergeometric Functions ◽  
New Class ◽  
Coefficient Bound ◽  
Characterization Property

We introduce a new subclass of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution). A characterization property such as the coefficient bound is obtained for this class. The other related properties, which are investigated in this paper, include the distortion and the radius of starlikeness. We also consider several applications of our main results to the generalized hypergeometric functions.

scholarly journals A Study of Cho-Kwon-Srivastava Operator with Applications to Generalized Hypergeometric Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
F. Ghanim ◽  
M. Darus
Keyword(s):  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Hadamard Product ◽  
The Other ◽  
Generalized Hypergeometric Functions ◽  
Coefficient Bounds ◽  
New Class ◽  
Characterization Property ◽  
Class Of Functions

We introduce a new class of meromorphically analytic functions, which is defined by means of a Hadamard product (or convolution) involving some suitably normalized meromorphically functions related to Cho-Kwon-Srivastava operator. A characterization property giving the coefficient bounds is obtained for this class of functions. The other related properties, which are investigated in this paper, include distortion and the radii of starlikeness and convexity. We also consider several applications of our main results to 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 Subordination and superordination results of p-valent analytic functions involving a linear operator

2017 ◽  
Vol 35 (2) ◽  
pp. 223 ◽  
Author(s):  
Tamer M. Seoudy
Keyword(s):  
Linear Operator ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc

In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of a linear operator. Some of our results improve and generalize previously known results.

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.

scholarly journals Mapping properties for convolutions involving hypergeometric functions

2003 ◽  
Vol 2003 (17) ◽  
pp. 1083-1091 ◽  
Author(s):  
J. A Kim ◽  
K. H. Shon
Keyword(s):  
Linear Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Hypergeometric Functions ◽  
Open Unit ◽  
Open Unit Disk

Forμ≥0, we consider a linear operatorLμ:A→Adefined by the convolutionfμ∗f, wherefμ=(1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Letφ∗(A,B)denote the class of normalized functionsfwhich are analytic in the open unit disk and satisfy the conditionzf′/f≺(1+Az)/1+Bz,−1≤A<B≤1, and letRη(β)denote the class of normalized analytic functionsffor which there exits a numberη∈(−π/2,π/2)such thatRe(eiη(f′(z)−β))>0,(β<1). The main object of this paper is to establish the connection betweenRη(β)andφ∗(A,B)involving the operatorLμ(f). Furthermore, we treat the convolutionI=∫0z(fμ(t)/t)dt ∗f(z)forf∈Rη(β).

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