scholarly journals Certain Subclasses of β-Uniformly q-Starlike and β-Uniformly q-Convex Functions

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Eman S. A. AbuJarad ◽  
Mohammed H. A. AbuJarad ◽  
Thabet Abdeljawad ◽  
Fahd Jarad
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Coefficient Bounds

In this paper, the authors introduced certain subclasses β-uniformly q-starlike and β-uniformly q-convex functions of order α involving the q-derivative operator defined in the open unit disc. Coefficient bounds were also investigated.

COEFFICIENT BOUNDS FOR A CERTAIN SUBCLASS OF CLOSE-TO-CONVEX FUNCTIONS ASSOCIATED WITH THE KOEBE FUNCTION

2018 ◽  
Vol 3 (2) ◽  
pp. 172
Author(s):  
Sidik Bin Rathi ◽  
Shaharuddin Cik Soh ◽  
Ajab Akbarally
Keyword(s):  
Convex Function ◽  
Convex Functions ◽  
Representation Theorem ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Koebe Function ◽  
Coefficient Bounds

We consider here the functions  which are analytic and univalent in the open unit disc  normalized by   and . By , we denote a new subclass of close-to-convex function such that  for which  and . In this paper, we give the representation theorem and obtain the coefficient bounds for functions in 

Further results for two certain subclasses of close-to-convex functions

2020 ◽  
pp. 2150045
Author(s):  
H. Mahzoon ◽  
R. Kargar
Keyword(s):  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
The Family ◽  
Radius Of Univalence

Let [Formula: see text] be the family of analytic and normalized functions [Formula: see text] in the open unit disc [Formula: see text]. In this paper, we consider the following classes: [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text] and [Formula: see text]. We show that if [Formula: see text], then [Formula: see text] and [Formula: see text] are greater than [Formula: see text], and if [Formula: see text], then [Formula: see text]. Also, some another interesting properties of the class [Formula: see text] are investigated. Finally, the radius of univalence of 2nd section sum of [Formula: see text] is obtained.

scholarly journals Convolution Properties for Certain Classes of Analytic Functions Defined byq-Derivative Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
T. M. Seoudy ◽  
M. K. Aouf
Keyword(s):  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Convolution Properties

We investigate convolution properties and coefficients estimates for two classes of analytic functions involving theq-derivative operator defined in the open unit disc. Some of our results improve previously known results.

scholarly journals Certain Conditions for Starlikeness of Analytic Functions of Koebe Type

2011 ◽  
Vol 2011 ◽  
pp. 1-12
Author(s):  
Saibah Siregar ◽  
Maslina Darus
Keyword(s):  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Open Unit Disc ◽  
Subordination Result ◽  
Jack’S Lemma ◽  
Jack's Lemma

For , , we consider the of normalized analytic convex functions defined in the open unit disc . In this paper, we investigate the class , that is, , with is Koebe type, that is, . The subordination result for the aforementioned class will be given. Further, by making use of Jack's Lemma as well as several differential and other inequalities, the authors derived sufficient conditions for starlikeness of the class of -fold symmetric analytic functions of Koebe type. Relevant connections of the results presented here with those given in the earlier works are also indicated.

scholarly journals Hankel determinant for certain class of analytic function defined by generalized derivative operator

2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Upper Bound ◽  
Unit Disc ◽  
Univalent Functions ◽  
Open Unit ◽  
Hankel Determinant ◽  
Open Unit Disc ◽  
Derivative Operator ◽  
Generalized Derivative ◽  
Generalised Derivatives

The authors in \cite{mam1} have recently introduced a new generalised derivatives operator $ \mu_{\lambda _1 ,\lambda _2 }^{n,m},$ which generalised many well-known operators studied earlier by many different authors. By making use of the generalised derivative operator $\mu_{\lambda_1 ,\lambda _2 }^{n,m}$, the authors derive the class of function denoted by $ \mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$, which contain normalised analytic univalent functions $f$ defined on the open unit disc $U=\left\{{z\,\in\mathbb{C}:\,\left| z \right|\,<\,1} \right\}$ and satisfy \begin{equation*}{\mathop{\rm Re}\nolimits} \left( {\mu _{\lambda _1 ,\lambda _2 }^{n,m} f(z)} \right)^\prime > 0,\,\,\,\,\,\,\,\,\,(z \in U).\end{equation*}This paper focuses on attaining sharp upper bound for the functional $\left| {a_2 a_4 - a_3^2 } \right|$ for functions $f(z)=z+ \sum\limits_{k = 2}^\infty {a_k \,z^k }$ belonging to the class $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.

A generalized class of α-convex functions with respect to n-symmetric points

2021 ◽  
pp. 2250099
Author(s):  
A. Y. Lashin ◽  
F. Z. El-Emam
Keyword(s):  
Integral Representation ◽  
Convex Functions ◽  
Analytic Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Symmetric Points

In this paper, we investigate certain subclass of analytic functions on the open unit disc. This class generalizes the well-known class of [Formula: see text]-convex functions with respect to n-symmetric points. Some interesting properties such as subordination results, containment relations, integral preserving properties, and the integral representation for functions in this class are obtained.

scholarly journals Coefficient Bounds for Certain Subclasses of Bi-Univalent Function

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
G. Murugusundaramoorthy ◽  
N. Magesh ◽  
V. Prameela
Keyword(s):  
Univalent Function ◽  
Unit Disc ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bounds

We introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients|a2|and|a3|for functions in these new subclasses. Also consequences of the results are pointed out.

scholarly journals Coefficient Bounds for Al-Oboudi Type Bi-univalent Functions based on a Modified Sigmoid Activation Function and Horadam Polynomials

2021 ◽  
pp. 251-270
Author(s):  
S. R. Swamy
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Activation Function ◽  
Type Operator ◽  
Open Unit ◽  
Open Unit Disc ◽  
Coefficient Bounds ◽  
Sigmoid Activation Function

Using the Al-Oboudi type operator, we present and investigate two special families of bi-univalent functions in $\mathfrak{D}$, an open unit disc, based on $\phi(s)=\frac{2}{1+e^{-s} },\,s\geq0$, a modified sigmoid activation function (MSAF) and Horadam polynomials. We estimate the initial coefficients bounds for functions of the type $g_{\phi}(z)=z+\sum\limits_{j=2}^{\infty}\phi(s)d_jz^j$ in these families. Continuing the study on the initial cosfficients of these families, we obtain the functional of Fekete-Szeg\"o for each of the two families. Furthermore, we present few interesting observations of the results investigated.

scholarly journals Radius Problems for Starlike Functions Associated with the Tan Hyperbolic Function

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Khalil Ullah ◽  
Saira Zainab ◽  
Muhammad Arif ◽  
Maslina Darus ◽  
Meshal Shutaywi
Keyword(s):  
Holomorphic Function ◽  
Convex Functions ◽  
Unit Disc ◽  
Starlike Functions ◽  
Open Unit ◽  
Hyperbolic Function ◽  
Open Unit Disc ◽  
Starlike And Convex Functions ◽  
Radius Problems

The aim of this particular article is at studying a holomorphic function f defined on the open-unit disc D = z ∈ ℂ : z < 1 for which the below subordination relation holds z f ′ z / f z ≺ q 0 z = 1 + tan h z . The class of such functions is denoted by S tan h ∗ . The radius constants of such functions are estimated to conform to the classes of starlike and convex functions of order β and Janowski starlike functions, as well as the classes of starlike functions associated with some familiar functions.

scholarly journals Coefficient inequality for transforms of starlike and convex functions

2015 ◽  
Vol 24 (1) ◽  
pp. 69-75
Author(s):  
D. VAMSHEE KRISHNA ◽  
◽  
B. VENKATESWARLU ◽  
T. RAMREDDY ◽  
◽  
...  
Keyword(s):  
Analytic Function ◽  
Complex Plane ◽  
Upper Bound ◽  
Convex Functions ◽  
Unit Disc ◽  
Open Unit ◽  
Open Unit Disc ◽  
Toeplitz Determinants ◽  
Starlike And Convex Functions ◽  
Coefficient Inequality

The objective of this paper is to obtain an upper bound for the second Hankel functional associated with the k th root transform ... normalized analytic function f(z) belonging to starlike and convex functions, defined on the open unit disc in the complex plane, using Toeplitz determinants.

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