scholarly journals On a subclass of close-to-convex harmonic mappings

2020 ◽  
pp. 2150102
Author(s):  
Rajbala ◽  
Jugal K. Prajapat
Keyword(s):  
Unit Disk ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class ◽  
Radius Of Convexity

In this paper, we introduce a new class of sense preserving harmonic mappings [Formula: see text] in the open unit disk and prove that functions in this class are close-to-convex. We give some basic properties such as coefficient bounds, growth estimates, convolution and determine the radius of convexity for the sections of functions belonging to this family. In addition, we construct certain harmonic univalent polynomials belonging to this family.

A New Subclass of Harmonic Univalent Functions

2017 ◽  
Vol 9 (2) ◽  
pp. 26-32
Author(s):  
Waggas Galib Atshan ◽  
Najah Ali Jiben Al-Ziadi
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Convex Combination ◽  
Univalent Functions ◽  
Extreme Points ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Basic Properties ◽  
New Class

In this paper, we define a new class of harmonic univalent functions of the form  in the open unit disk . We obtain basic properties, like, coefficient bounds, extreme points, convex combination, distortion and growth theorems and integral operator.

scholarly journals On a class of analytic functions governed by subordination

2019 ◽  
Vol 11 (1) ◽  
pp. 144-155 ◽  
Author(s):  
Ravinder Krishna Raina ◽  
Janusz Sokół
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Basic Properties ◽  
Radius Of Convexity ◽  
Class Of Functions

Abstract The purpose of this paper is to introduce a class of functions ℱλ, λ ∈ [0, 1], consisting of analytic functions f normalized by f(0) = f´(0) − 1 = 0 in the open unit disk U which satisfies the subordination condition that $${\rm{z}}f'\left( {\rm{z}} \right)/\left\{ {\left( {1 - \lambda } \right){\rm{f}}\left( {\rm{z}} \right) + \lambda {\rm{z}}} \right\} \prec {\rm{q}}\left( {\rm{z}} \right),\,\,\,\,\,{\rm{z}} \in {\rm{\mathbb{U},}}$$ where ${\rm{q}}\left( {\rm{z}} \right) = \sqrt {1 + {{\rm{z}}^{\rm{2}}}} + {\rm{z}}$ . Some basic properties (including the radius of convexity) are obtained for this class of functions.

On a Subclass of Univalent Harmonic Mappings Convex in the Imaginary Direction

2020 ◽  
pp. 445-454
Author(s):  
Deepali Khurana ◽  
Sushma Gupta ◽  
Sukhjit Singh
Keyword(s):  
Present Article ◽  
Unit Disk ◽  
Imaginary Axis ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Distortion Bounds ◽  
Univalent Harmonic Mappings

In the present article, we consider a class of univalent harmonic mappings, $\mathcal{C}_{T} = \left\{ T_{c}[f] =\frac{f+czf'}{1+c}+\overline{\frac{f-czf'}{1+c}}; \; c>0\;\right\}$ and $f$ is convex univalent in $\mathbb{D}$, whose functions map the open unit disk $\mathbb{D}$ onto a domain convex in the direction of the imaginary axis. We estimate coefficient, growth and distortion bounds for the functions of the same class.

scholarly journals Coefficient bounds for certain subclasses of bi-prestarlike functions associated with the Chebyshev polynomials

2020 ◽  
Vol 24 (2) ◽  
pp. 71-82
Author(s):  
H.Ö. Güney ◽  
G. Murugusundaramoorthy ◽  
K. Vijaya ◽  
K. Thilagavathi
Keyword(s):  
Unit Disk ◽  
Chebyshev Polynomials ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds

In this paper, we introduce and investigate a new subclass of bi-prestarlike functions defined in the open unit disk, associated with Chebyshev Polynomials. Furthermore, we find estimates of first two coefficients of functions in these classes, making use of the Chebyshev polynomials. Also, we obtain the Fekete-Szegö inequalities for function in these classes. Several consequences of the results are also pointed out as corollaries.

scholarly journals Some general coefficient estimates for a new class of analytic and bi-univalent functions defined by a linear combination

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem
Keyword(s):  
Linear Combination ◽  
Unit Disk ◽  
Univalent Function ◽  
Univalent Functions ◽  
Function Class ◽  
Open Unit ◽  
Faber Polynomials ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
New Class

In the present paper, we introduce and investigate a new class of analytic and bi-univalent functions f (z) in the open unit disk U. For this purpose, we make use of a linear combination of the following three functions: f(z)/z, f'(z) and z f''(z) for a function belonging to the normalized univalent function class S. By applying the technique involving the Faber polynomials, we determine estimates for the general Taylor-Maclaurin coefficient of functions belonging to the analytic and bi-univalent function class which we have introduced here. We also demonstrate the not-too-obvious behaviour of the first two Taylor-Maclaurin coefficients of such functions.

scholarly journals Argument and Coefficient Estimates for Certain Analytic Functions

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 88 ◽  
Author(s):  
Davood Alimohammadi ◽  
Nak Eun Cho ◽  
Ebrahim Analouei Adegani ◽  
Ahmad Motamednezhad
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Sharp Bounds ◽  
New Class ◽  
Logarithmic Coefficients

The aim of the present paper is to introduce a new class G α , δ of analytic functions in the open unit disk and to study some properties associated with strong starlikeness and close-to-convexity for the class G α , δ . We also consider sharp bounds of logarithmic coefficients and Fekete-Szegö functionals belonging to the class G α , δ . Moreover, we provide some topics related to the results reported here that are relevant to outcomes presented in earlier research.

scholarly journals Composition Operators on Some Banach Spaces of Harmonic Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Spaces Of Analytic Functions

We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.

ON THE HARMONIC ZYGMUND SPACES

2020 ◽  
Vol 101 (3) ◽  
pp. 466-476
Author(s):  
MUNIRAH ALJUAID ◽  
FLAVIA COLONNA
Keyword(s):  
Unit Disk ◽  
Complex Plane ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Class A ◽  
Analytic Case ◽  
Separable Subspace ◽  
Zygmund Spaces

In this paper we study a class ${\mathcal{Z}}_{H}$ of harmonic mappings on the open unit disk $\mathbb{D}$ in the complex plane that is an extension of the classical (analytic) Zygmund space. We extend to the elements of this class a characterisation that is valid in the analytic case. We also provide a similar result for a closed separable subspace of ${\mathcal{Z}}_{H}$ which we call the little harmonic Zygmund space.

scholarly journals Coefficient bounds for new subclasses of analytic and m-fold symmetric bi-univalent functions

2021 ◽  
Vol 66 (4) ◽  
pp. 659-666
Author(s):  
Abbas Kareem Wanas ◽  
◽  
Agnes Orsolya Pall-Szabo ◽  
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Special Cases

In the present paper, we introduce and study two new subclasses of analytic and $m$-fold symmetric bi-univalent functions defined in the open unit disk $U$. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients $\left| a_{m+1}\right|$ and $\left| a_{2m+1}\right|$. Also, we indicate certain special cases for our results.

scholarly journals Initial coefficient bounds for a subclass of m-fold symmetric bi-univalent functions

2021 ◽  
Vol 39 (4) ◽  
pp. 153-164
Author(s):  
Ahmad Zireh ◽  
Saideh Hajiparvaneh
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Bounds ◽  
Initial Coefficient

‎In this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

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