The order of starlikeness of uniformly convex functions

2017 ◽  
Vol 23 (1) ◽  
Author(s):  
Agnieszka Wiśniowska-Wajnryb
Keyword(s):  
Convex Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions ◽  
Order Of Starlikeness

AbstractWe investigate classes of

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.

scholarly journals Uniformly convex functions

1992 ◽  
Vol 57 (2) ◽  
pp. 165-175 ◽  
Author(s):  
Wancang Ma ◽  
David Minda
Keyword(s):  
Convex Functions ◽  
Uniformly Convex ◽  
Uniformly Convex Functions
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