scholarly journals Subclasses of Starlike Functions Associated with Fractional q-Calculus Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
C. Selvaraj ◽  
O. S. Babu
Keyword(s):  
Extreme Points ◽  
Starlike Functions ◽  
Partial Sums ◽  
Coefficient Estimate ◽  
Integral Means ◽  
Closure Theorem ◽  
Distortion Bounds

Making use of fractional q-calculus operators, we introduce a new subclass ℳq(λ,γ,k) of starlike functions and determine the coefficient estimate, extreme points, closure theorem, and distortion bounds for functions in ℳq(λ,γ,k). Furthermore we discuss neighborhood results, subordination theorem, partial sums, and integral means inequalities for functions in ℳq(λ,γ,k).

A Class of Harmonic Starlike Functions defined by Multiplier Transformation

2020 ◽  
pp. 455-469
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin
Keyword(s):  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Harmonic Mappings ◽  
Distortion Bounds ◽  
Radius Of Convexity ◽  
Univalent Harmonic Mappings ◽  
Harmonic Starlike ◽  
Multiplier Transformation

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.

scholarly journals On Certain Subclass of Harmonic Starlike Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin
Keyword(s):  
Integral Operator ◽  
Unit Disc ◽  
Univalent Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disc ◽  
New Class ◽  
Distortion Bounds ◽  
Harmonic Starlike

Coefficient conditions, distortion bounds, extreme points, convolution, convex combinations, and neighborhoods for a new class of harmonic univalent functions in the open unit disc are investigated. Further, a class preserving integral operator and connections with various previously known results are briefly discussed.

scholarly journals A New Class of Analytic Functions Defined by Using Salagean Operator

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
R. M. El-Ashwah ◽  
M. K. Aouf ◽  
A. A. M. Hassan ◽  
A. H. Hassan
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Distortion Theorem ◽  
Partial Sums ◽  
Coefficient Estimates ◽  
Integral Means ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Fractional Calculus Operators

We derive some results for a new class of analytic functions defined by using Salagean operator. We give some properties of functions in this class and obtain numerous sharp results including for example, coefficient estimates, distortion theorem, radii of star-likeness, convexity, close-to-convexity, extreme points, integral means inequalities, and partial sums of functions belonging to this class. Finally, we give an application involving certain fractional calculus operators that are also considered.

scholarly journals Q-Extension of Starlike Functions Subordinated with a Trigonometric Sine Function

Mathematics ◽  
2020 ◽  
Vol 8 (10) ◽  
pp. 1676
Author(s):  
Saeed Islam ◽  
Muhammad Ghaffar Khan ◽  
Bakhtiar Ahmad ◽  
Muhammad Arif ◽  
Ronnason Chinram
Keyword(s):  
Extreme Point ◽  
Point Theorem ◽  
Starlike Functions ◽  
Partial Sums ◽  
Sufficient Condition ◽  
Sine Function ◽  
Necessary And Sufficient Condition ◽  
Closure Theorem ◽  
Necessary And Sufficient ◽  
Distortion Bound

The main purpose of this article is to examine the q-analog of starlike functions connected with a trigonometric sine function. Further, we discuss some interesting geometric properties, such as the well-known problems of Fekete-Szegö, the necessary and sufficient condition, the growth and distortion bound, closure theorem, convolution results, radii of starlikeness, extreme point theorem and the problem with partial sums for this class.

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.

scholarly journals New classes of $k$-uniformly convex and starlike functions

2004 ◽  
Vol 35 (3) ◽  
pp. 261-266 ◽  
Author(s):  
Essam Aqlan ◽  
Jay M. Jahangiri ◽  
S. R. Kulkarni
Keyword(s):  
Analytic Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Uniformly Convex ◽  
Radius Of Starlikeness ◽  
Distortion Bounds ◽  
Convex And Starlike Functions

Certain classes of analytic functions are defined which will generalize new, as well as well-known, classes of k-uniformly convex and starlike functions. We provide necessary and sufficent coefficient conditions, distortion bounds, extreme points and radius of starlikeness for these classes.

scholarly journals A class of bounded starlike functions

1994 ◽  
Vol 17 (2) ◽  
pp. 249-252 ◽  
Author(s):  
Herb Silverman
Keyword(s):  
Unit Disk ◽  
Lower Bounds ◽  
Extreme Points ◽  
Starlike Functions ◽  
Partial Sums

We consider functionsf(z)=z+…that are analytic in the unit disk and satisfy there the inequalityRe(f′(z)+zf″(z))>α,α<1. We find extreme points and then determine sharp lower bounds onRef′(z)andRe(f(z)/z). Sharp results for the sequence of partial sums are also found.

scholarly journals On a Subclass of Meromorphic Functions Defined by Hilbert Space Operator

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Thomas Rosy ◽  
S. Sunil Varma
Keyword(s):  
Hilbert Space ◽  
Meromorphic Functions ◽  
Extreme Points ◽  
Operator Coefficient ◽  
Coefficient Estimate ◽  
Space Operator ◽  
Hilbert Space Operator ◽  
Distortion Bounds

In this paper, we define a new operator on the class of meromorphic functions and define a subclass using Hilbert space operator. Coefficient estimate, distortion bounds, extreme points, radii of starlikeness, and convexity are obtained.

scholarly journals Starlike functions of complex order involving q-hypergeometric functions with fixed point

2014 ◽  
Vol 13 (1) ◽  
pp. 51-63
Author(s):  
Kaliappan Vijaya ◽  
Gangadharan Murugusundaramoorthy ◽  
Murugesan Kasthuri
Keyword(s):  
Fixed Point ◽  
Hypergeometric Functions ◽  
Extreme Points ◽  
Starlike Functions ◽  
Function Class ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Open Disc ◽  
Starlike And Convex Functions ◽  
Complex Order

AbstractRecently Kanas and Ronning introduced the classes of starlike and convex functions, which are normalized with ƒ(ξ) = ƒ0(ξ) − 1 = 0, ξ (|ξ| = d) is a fixed point in the open disc U = {z ∈ ℂ: |z| < 1}. In this paper we define a new subclass of starlike functions of complex order based on q-hypergeometric functions and continue to obtain coefficient estimates, extreme points, inclusion properties and neighbourhood results for the function class T Sξ(α, β,γ). Further, we obtain integral means inequalities for the function ƒ ∈ T Sξ(α, β,γ).

Some properties for certain subclasses of analytic functions defined by a general differential operator

2019 ◽  
Vol 13 (07) ◽  
pp. 2050134
Author(s):  
Erhan Deniz ◽  
Murat Çağlar ◽  
Yücel Özkan
Keyword(s):  
Differential Operator ◽  
Analytic Functions ◽  
Partial Sums ◽  
Integral Means

In this paper, we study two new subclasses [Formula: see text] and [Formula: see text] of analytic functions which are defined by means of a differential operator. Some results connected to partial sums and neighborhoods and integral means related to these subclasses are obtained.

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