scholarly journals On Subclass of -Uniformly Convex Functions of Complex Order Involving Multiplier Transformations

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Waggas Galib Atshan ◽  
Ali Hamza Abada
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Integral Means ◽  
Uniformly Convex Functions ◽  
Complex Order

We introduce a subclass of -uniformly convex functions of order with negative coefficients by using the multiplier transformations in the open unit disk . We obtain coefficient estimates, radii of convexity and close-to-convexity, extreme points, and integral means inequalities for the function that belongs to the 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 Topological Properties for Harmonic τ-Uniformly Convex Functions of Order ρ Associated with Wanas Differential Operator

2020 ◽  
pp. 333-346
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Differential Operator ◽  
Unit Disk ◽  
Convex Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Uniformly Convex ◽  
Topological Properties ◽  
Uniformly Convex Functions

The purpose of the present paper is to establish some topological properties for a certain family of harmonic τ-uniformly convex functions of order ρ associated with Wanas differential operator defined in the open unit disk U.

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

scholarly journals Coefficient Estimates of Bi-Starlike and Bi-Convex Functions with Respect to Symmetrical Points Associated with the Second Kind Chebyshev Polynomials

2020 ◽  
pp. 191-198
Author(s):  
Abbas Kareem Wanas
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Convex Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Symmetrical Points

In this paper, by making use the second kind Chebyshev polynomials, we introduce and study a certain class of bi-starlike and bi-convex functions with respect to symmetrical points defined in the open unit disk. We find upper bounds for the second and third coefficients of functions belong to this class.

On a subclass of uniformly convex functions with fixed second coefficient

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
H. E. Darwish
Keyword(s):  
Convex Functions ◽  
Extreme Points ◽  
Uniformly Convex ◽  
Coefficient Estimates ◽  
Uniformly Convex Functions ◽  
New Class ◽  
Sălăgean Operator ◽  
Salagean Operator ◽  
Distortion Bounds ◽  
Closure Theorems

AbstractUsing of Salagean operator, we define a new subclass of uniformly convex functions with negative coefficients and with fixed second coefficient. The main objective of this paper is to obtain coefficient estimates, distortion bounds, closure theorems and extreme points for functions belonging of this new class. The results are generalized to families with fixed finitely many coefficients.

scholarly journals Coefficient, distortion and growth inequalities for certain p-valent close-to-convex functions

2013 ◽  
Vol 9 (2) ◽  
pp. 57-62
Author(s):  
I.B. Bapana ◽  
Sneha Handwana
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Distortion Theorems

Abstract In the present paper, we introduce and investigate a new subclass χtp(γ) of analytic and p-valent close-to-convex functions in the open unit disk U. For functions belonging to the class χtp(γ), some interesting properties including the coefficient estimates, distortion theorems and subordination results are obtained

Coefficient Estimates for Certain Subclasses of m-Fold Symmetric Bi-univalent Functions Associated with Pseudo-Starlike Functions

2021 ◽  
pp. 209-223
Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil
Keyword(s):  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Starlike Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In the present investigation, we introduce the subclasses $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\phi)$ and $\varLambda_{\Sigma}^{m}(\eta,\leftthreetimes,\delta)$ of \textit{m}-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the pseudo-starlike functions and defined in the open unit disk $\mathbb{U}$. Moreover, we obtain estimates on the initial coefficients $|b_{m+1}|$ and $|b_{2m+1}|$ for the functions belong to these subclasses and identified correlations with some of the earlier known classes.

scholarly journals On Certain Classes of Convex Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Young Jae Sim ◽  
Oh Sang Kwon
Keyword(s):  
Unit Disk ◽  
Convex Functions ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Real Numbers ◽  
Inverse Functions

For real numbersαandβsuch that0≤α<1<β, we denote by𝒦α,βthe class of normalized analytic functions which satisfy the following two sided-inequality:α<ℜ1+zf′′z/f′z<β  z∈𝕌,where𝕌denotes the open unit disk. We find some relationships involving functions in the class𝒦(α,β). And we estimate the bounds of coefficients and solve the Fekete-Szegö problem for functions in this class. Furthermore, we investigate the bounds of initial coefficients of inverse functions or biunivalent functions.

scholarly journals Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1334
Author(s):  
Bilal Khan ◽  
Hari M. Srivastava ◽  
Nazar Khan ◽  
Maslina Darus ◽  
Muhammad Tahir ◽  
...  
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Second Order ◽  
Open Unit ◽  
Open Unit Disk ◽  
Hankel Determinant ◽  
Coefficient Estimates ◽  
Principle Of Subordination

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

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