scholarly journals Mapping properties of certain linear operator associated with hypergeometric functions

2021 ◽  
Vol 39 (2) ◽  
pp. 223-236
Author(s):  
T. Panigrahi ◽  
R. El-Ashwah
Keyword(s):  
Linear Operator ◽  
Integral Operator ◽  
Convex Function ◽  
Convex Functions ◽  
Hypergeometric Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Uniformly Starlike

The main object of the present paper is to …nd some su¢ cient conditions in terms of hypergeometric inequalities so that the linear operator denoted by Ha;b;c : maps a certain subclass of close-to-convex function R (A;B) into subclasses of k-uniformly starlike and k-uniformly convex functions k 􀀀ST () and k 􀀀UCV() respectively. Further, we consider an integral operator and discuss its properties. Our results generalize some relevant results.

A unified class of k-uniformly convex functions defined by the Dziok–Srivastava linear operator

2007 ◽  
Vol 190 (2) ◽  
pp. 1627-1636 ◽  
Author(s):  
C. Ramachandran ◽  
T.N. Shanmugam ◽  
H.M. Srivastava ◽  
A. Swaminathan
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions

scholarly journals Certain New Classes of Analytic Functions with Varying Arguments

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Uniformly Starlike Functions ◽  
Uniformly Starlike ◽  
Varying Arguments

We introduce certain new classes κ−VST(α,β) and κ−VUCV(α,β), which represent the κ uniformly starlike functions of order α and type β with varying arguments and the κ uniformly convex functions of order α and type β with varying arguments, respectively. Moreover, we give coefficients estimates, distortion theorems, and extreme points of these classes.

scholarly journals On a subclass of β-uniformly convex functions defined by Dziok-Srivastava linear operator

2007 ◽  
Vol 3 (2) ◽  
Author(s):  
Jamal M. Shenan
Keyword(s):  
Linear Operator ◽  
Fractional Derivative ◽  
Convex Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Fractional Derivative Operators

In this paper a new subclass of uniformly convex functions with negative coefficients defined by Dziok-Srivastava Linear operator is introduced. Characterization properties exhibited by certain fractional derivative operators of functions and the result of modified Hadmard product are discussed for this class. Further class preserving ntegral operator, extreme points and other interesting properties for this class are also indicated. 2000mathematics Subj. Classification: 30C45, 26A33.

scholarly journals Applications of fractional calculus to $ k $-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $

2007 ◽  
Vol 38 (2) ◽  
pp. 103-109 ◽  
Author(s):  
Ajab Akbarally ◽  
Maslina Darus
Keyword(s):  
Fractional Calculus ◽  
Convex Functions ◽  
Analytic Functions ◽  
Uniformly Convex ◽  
Coefficient Bounds ◽  
Uniformly Convex Functions ◽  
Distortion Theorems ◽  
Growth And Distortion Theorems ◽  
Uniformly Starlike

A new subclass of analytic functions $ k-SP_\lambda(\alpha) $ is introduced by applying certain operators of fractional calculus to $k$-uniformly starlike and $ k $-uniformly convex functions of order $ \alpha $. Some theorems on coefficient bounds and growth and distortion theorems for this subclass are found. The radii of close to convexity, starlikeness and convexity for this subclass is also derived.

scholarly journals Certain Subclasses of Starlike Functions of Complex Order Involving Generalized Hypergeometric Functions

2010 ◽  
Vol 2010 ◽  
pp. 1-12 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Generalized Hypergeometric Functions ◽  
Uniformly Convex Functions

Making use of the generalized hypergeometric functions, we define a new subclass of uniformly convex functions and a corresponding subclass of starlike functions with negative coefficients and obtain coefficient estimates, extreme points, the radii of close-to-convexity, starlikeness and convexity, and neighborhood results for the classTSml(α,β,γ). In particular, we obtain integral means inequalities for the functionfthat belongs to the classTSml(α,β,γ)in the unit disc.

Sign in / Sign up

Export Citation Format

Share Document