scholarly journals Subclass of uniformly convex functions defined by linear operator

2017 ◽  
Vol 263 ◽  
pp. 042157
Author(s):  
A Narasimha Murthy ◽  
H Niranjan ◽  
P Thirupathi Reddy
Keyword(s):  
Linear Operator ◽  
Convex Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions

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 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.

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 ON SUBCLASSES OF UNIFORMLY CONVEX FUNCTIONS AND CORRESPONDING CLASS OF STARLIKE FUNCTIONS

1997 ◽  
Vol 28 (1) ◽  
pp. 17-32
Author(s):  
R. BHARATI ◽  
R. PARVATHAM ◽  
A. SWAMINATHAN
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Sufficient Condition ◽  
Uniformly Convex ◽  
Uniformly Convex Functions

We determine a sufficient condition for a function $f(z)$ to be uniformly convex of order et that is also necessary when $f(z)$ has negative coefficients. This enables us to express these classes of functions in terms of convex functions of particular order. Similar results for corresponding classes of starlike functions are also obtained. The convolution condition for the above two classes are discussed.

Some properties of a subclass of uniformly convex functions with negative coefficients

2008 ◽  
Vol 41 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. O. Mostafa
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions

AbstractThe aim of this paper is to obtain coefficient estimates, distortion theorem, extreme points and radii of close - to - convexity, starlikeness and convexity for functions belonging to the subclass

Pre-Schwarzian norm for linear operators of uniformly convex functions of order α and type β

2019 ◽  
Vol 56 (3) ◽  
pp. 297-308
Author(s):  
Jacek Dziok ◽  
Hanaa M. Zayed
Keyword(s):  
Convex Functions ◽  
Schwarzian Derivative ◽  
Linear Operators ◽  
New Method ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Norm Estimates

Abstract By making use of the pre-Schwarzian norm given by we obtain such norm estimates for Hohlov operator of functions belonging to the class of uniformly convex functions of order α and type β. We also employ an entirely new method to generalize and extend the results of Theorems 1, 2 and 3 in [3]. Finally, some inequalities concerning the norm of the pre-Schwarzian derivative for Dziok-Srivastava operator are also considered.

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