The q-difference operator associated with the multivalent function bounded by conical sections

2021 ◽  
Vol 39 (1) ◽  
pp. 133-146
Author(s):  
C. Ramachandran ◽  
S. Annamalai ◽  
Basem Frasin
Keyword(s):  
Convex Functions ◽  
Difference Operator ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Multivalent Function ◽  
Uniformly Convex Functions ◽  
Ruscheweyh Derivative ◽  
Inclusion Relations

In this paper we obtain some inclusion relations of k - starlike functions, k - uniformly convex functions and quasi-convex functions. Furthermore, we obtain coe¢ cient bounds for some subclasses of fractional q-derivative multivalent functions together with generalized Ruscheweyh derivative.

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.

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 Radii of starlikeness and convexity for functions with fixed second coefficient defined by subordination

Filomat ◽  
2012 ◽  
Vol 26 (3) ◽  
pp. 553-561 ◽  
Author(s):  
Rosihan Ali ◽  
Eun Cho ◽  
Kumar Jain ◽  
V. Ravichandran
Keyword(s):  
Convex Functions ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Uniformly Convex Functions ◽  
Lemniscate Of Bernoulli ◽  
Strongly Starlike Functions ◽  
Special Cases ◽  
Radius Of Convexity ◽  
Strongly Starlike

Several radii problems are considered for functions f (z) = z + a2z2 + ... with fixed second coefficient a2. For 0 ? ? < 1, sharp radius of starlikeness of order ? for several subclasses of functions are obtained. These include the class of parabolic starlike functions, the class of Janowski starlike functions, and the class of strongly starlike functions. Sharp radius of convexity of order ? for uniformly convex functions, and sharp radius of strong-starlikeness of order ? for starlike functions associated with the lemniscate of Bernoulli are also obtained as special cases.

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.

A subclass of uniformly convex functions and a corresponding subclass of starlike function with fixed coefficient associated with q-analogue of Ruscheweyh operator

2019 ◽  
Vol 69 (4) ◽  
pp. 825-832 ◽  
Author(s):  
Shahid Khan ◽  
Saqib Hussain ◽  
Muhammad A. Zaighum ◽  
Maslina Darus
Keyword(s):  
Differential Operator ◽  
Extreme Point ◽  
Convex Functions ◽  
Starlike Functions ◽  
Starlike Function ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Closure Theorems

Abstract Making use of Ruscheweyh q-differential operator, we define a new subclass of uniformly convex functions and corresponding subclass of starlike functions with negative coefficients. The main object of this paper is to obtain, coefficient estimates, closure theorems and extreme point for the functions belonging to this new class. The results are generalized to families with fixed finitely many coefficients.

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