scholarly journals Certain class of bi-univalent functions defined by quantum calculus operator associated with Faber polynomial

2021 ◽  
Vol 7 (2) ◽  
pp. 2989-3005
Author(s):  
Sheza. M. El-Deeb ◽  
◽  
Gangadharan Murugusundaramoorthy ◽  
Kaliyappan Vijaya ◽  
Alhanouf Alburaikan ◽  
...  

<abstract><p>In this paper, we introduce a new class of bi-univalent functions defined in the open unit disc and connected with a $ q $-convolution. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class by using Faber polynomial expansions, and we obtain an estimation for Fekete-Szegö problem for this class.</p></abstract>

2019 ◽  
Vol 11 (1) ◽  
pp. 5-17 ◽  
Author(s):  
Om P. Ahuja ◽  
Asena Çetinkaya ◽  
V. Ravichandran

Abstract We study a family of harmonic univalent functions in the open unit disc defined by using post quantum calculus operators. We first obtained a coefficient characterization of these functions. Using this, coefficients estimates, distortion and covering theorems were also obtained. The extreme points of the family and a radius result were also obtained. The results obtained include several known results as special cases.


2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
A. Y. Lashin

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.


2020 ◽  
Vol 29 (1) ◽  
pp. 81-89
Author(s):  
F. MUGE SAKAR ◽  
H. OZLEM GUNEY

A function is said to be bi-univalent in the open unit disc D, if both the function f and its inverse are univalent in the unit disc. Besides, a function is said to be bi-Bazilevic in ˘ D, if both the function f and its inverse are Bazilevic there. The behaviour of these types of functions are unpredictable ˘ and not much is known about their coefficients. In this study, we determined coefficient estimates for the Taylor Maclaurin coefficients of the class on m-fold symmetric bi-Bazilevic functions. We also, use the Faber Polynomial expansions to obtain these coefficient estimates associated with ˘ upper bounds.


1973 ◽  
Vol 25 (2) ◽  
pp. 420-425 ◽  
Author(s):  
Douglas Michael Campbell

Let denote the set of all normalized analytic univalent functions in the open unit disc D. Let f(z), F(z) and φ(z) be analytic in |z| < r. We say that f(z) is majorized by F(z) in we say that f(z) is subordinate to F(z) in where .Let be the set of all locally univalent (f’(z) ≠ 0) analytic functions in D with order ≦α which are of the form f(z) = z +… . The family is known as the universal linear invariant family of order α [6]. A concise summary of and introduction to properties of linear invariant families which relate to the following material is contained in [1]. The present paper contains the proofs of some of the results announced in [1]


2017 ◽  
Vol 2017 ◽  
pp. 1-4
Author(s):  
Maslina Darus ◽  
Shigeyoshi Owa

Considering a function f(z)=z/1-z2 which is analytic and starlike in the open unit disc U and a function f(z)=z/1-z which is analytic and convex in U, we introduce two new classes Sα⁎(β) and Kα(β) concerning fα(z)=z/1-zα  (α>0). The object of the present paper is to discuss some interesting properties for functions in the classes Sα⁎(β) and Kα(β).


2021 ◽  
Vol 6 (12) ◽  
pp. 13235-13246
Author(s):  
Murugusundaramoorthy Gangadharan ◽  
◽  
Vijaya Kaliyappan ◽  
Hijaz Ahmad ◽  
K. H. Mahmoud ◽  
...  

<abstract><p>In this paper, we examine a connotation between certain subclasses of harmonic univalent functions by applying certain convolution operator regarding Mittag-Leffler function. To be more precise, we confer such influences with Janowski-type harmonic univalent functions in the open unit disc $ \mathbb{D}. $</p></abstract>


2020 ◽  
Vol 108 (122) ◽  
pp. 155-162
Author(s):  
Sibel Yalçın ◽  
Waggas Atshan ◽  
Haneen Hassan

We investigate specific new subclasses of the function class ? of bi-univalent function defined in the open unit disc, which is connected with quasi-subordination. We find estimates on the Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses. Already pointed out are some documented and new implications of those findings.


Filomat ◽  
2014 ◽  
Vol 28 (7) ◽  
pp. 1493-1503 ◽  
Author(s):  
Khalida Noor ◽  
Nazar Khan ◽  
Muhammad Noor

In this paper, we use the concept of bounded Mocanu variation to introduce a new class of analytic functions, defined in the open unit disc, which unifies a number of classes previously studied such as those of functions with bounded radius rotation and bounded Mocanu variation. It also generalizes the concept of ?-spiral likeness in some sense. Some interesting properties of this class including inclusion results, arclength problems and a sufficient condition for univalency are studied.


Filomat ◽  
2015 ◽  
Vol 29 (8) ◽  
pp. 1839-1845 ◽  
Author(s):  
H.M. Srivastava ◽  
Sevtap Eker ◽  
Rosihan Alic

In this paper, we introduce and investigate a subclass of analytic and bi-univalent functions in the open unit disk U. By using the Faber polynomial expansions, we obtain upper bounds for the coefficients of functions belonging to this analytic and bi-univalent function class. Some interesting recent developments involving other subclasses of analytic and bi-univalent functions are also briefly mentioned.


2012 ◽  
Vol 43 (3) ◽  
pp. 445-453
Author(s):  
Ma'moun Harayzeh Al-Abbadi ◽  
Maslina Darus

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 $\mathcal{H}_{\lambda _1 ,\lambda _2 }^{n,m}$.


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