scholarly journals Coefficient estimates for certain subclasses of analytic and bi-univalent functions

Filomat ◽  
2015 ◽  
Vol 29 (2) ◽  
pp. 351-360 ◽  
Author(s):  
Yong Sun ◽  
Yue-Ping Jiang ◽  
Antti Rasila
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

For ? ? 0 and 0 ? ? < 1 < ?, we denote by K(?,?,?) the class of normalized analytic functions satisfying the two sided-inequality ? < K (Zf'(z)/f(z) + z2f''(z)/f(z))<? (z ? U), where U is the open unit disk. Let K? (?, ?, ?) be the class of bi-univalent functions such that f and its inverse f-1 both belong to the class K(?, ?, ?). In this paper, we establish bounds for the coefficients, and solve the Fekete-Szeg? problem, for the class K((?,?,?). Furthermore, we obtain upper bounds for the first two Taylor-Maclaurin coefficients of the functions in the class K? (?,?,?)

scholarly journals Faber Polynomial Coefficient Estimates for Bi-Univalent Functions Defined by Using Differential Subordination and a Certain Fractional Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (2) ◽  
pp. 172 ◽  
Author(s):  
Hari M. Srivastava ◽  
Ahmad Motamednezhad ◽  
Ebrahim Analouei Adegani
Keyword(s):  
Fractional Derivative ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Faber Polynomial

In this article, we introduce a general family of analytic and bi-univalent functions in the open unit disk, which is defined by applying the principle of differential subordination between analytic functions and the Tremblay fractional derivative operator. The upper bounds for the general coefficients | a n | of functions in this subclass are found by using the Faber polynomial expansion. We have thereby generalized and improved some of the previously published results.

Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate

2018 ◽  
Vol 68 (2) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmad Zireh ◽  
Ebrahim Analouei Adegani ◽  
Mahmood Bidkham
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Polynomial Coefficient ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Faber Polynomial

Abstract In this paper, we use the Faber polynomial expansion to find upper bounds for |an| (n ≥ 3) coefficients of functions belong to classes $\begin{array}{} H_{q}^{\Sigma}(\lambda,h),\, ST_{q}^{\Sigma}(\alpha,h)\,\text{ and} \,\,M_{q}^{\Sigma}(\alpha,h) \end{array}$ which are defined by quasi-subordinations in the open unit disk 𝕌. Further, we generalize some of the previously published results.

scholarly journals Coefficient estimates for a new subclass of analytic and bi-univalent functions by Hadamard product

2021 ◽  
Vol 39 (2) ◽  
pp. 87-104
Author(s):  
Ebrahim Analouei Adegani ◽  
Ahmad Zireh ◽  
Mostafa Jafari
Keyword(s):  
Unit Disk ◽  
Hadamard Product ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In this work, we introduce a new subclas of bi-univalent functions which is defined by Hadamard product andsubordination in the open unit disk. and find upper bounds for the second and third coefficients for functions in this new subclass. Further, we generalize and improve some of the previously published results.

Coefficient Estimates for a Subclass of Bi-Univalent Functions Defined by q-Derivative Operator

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 306 ◽  
Author(s):  
Suhila Elhaddad ◽  
Maslina Darus
Keyword(s):  
Unit Disk ◽  
Systematic Study ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates ◽  
Derivative Operator ◽  
Coefficient Bounds ◽  
Coefficient Inequalities

Recently, a number of features and properties of interest for a range of bi-univalent and univalent analytic functions have been explored through systematic study, e.g., coefficient inequalities and coefficient bounds. This study examines S q δ ( ϑ , η , ρ , ν ; ψ ) as a novel general subclass of Σ which comprises normalized analytic functions, as well as bi-univalent functions within Δ as an open unit disk. The study locates estimates for the | a 2 | and | a 3 | Taylor–Maclaurin coefficients in functions of the class which is considered. Additionally, links with a number of previously established findings are presented.

Coefficient estimates for some subclasses of m-fold symmetric bi-univalent functions

Filomat ◽  
2018 ◽  
Vol 32 (9) ◽  
pp. 3143-3153
Author(s):  
H.M. Srivastava ◽  
Ahmad Zireh ◽  
Saideh Hajiparvaneh
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Upper Bounds ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

In this work, we introduce and investigate a subclass Hh,p ?m(?,?) of analytic and bi-univalent functions when both f(z) and f-1(z) are m-fold symmetric in the open unit disk U. Moreover, we find upper bounds for the initial coefficients |am+1| and |a2m+1| for functions belonging to this subclass Hh,p ?m(?,?). The results presented in this paper would generalize and improve those that were given in several recent works.

scholarly journals Certain subclass of analytic functions defined by means of differential subordination

Filomat ◽  
2016 ◽  
Vol 30 (14) ◽  
pp. 3743-3757 ◽  
Author(s):  
H.M. Srivastava ◽  
Dorina Răducanu ◽  
Paweł Zaprawa
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Differential Subordination ◽  
Open Unit ◽  
Open Unit Disk ◽  
Coefficient Estimates

For ??(?,?], let Ra(?) denote the class of all normalized analytic functions in the open unit disk U satisfying the following differential subordination: f'(z)+1/2(1+ei?)z f''(z)<?(z) z ? U), where the function ?(z) is analytic in the open unit disk U such that ?(0)=1. In this paper, various integral and convolution characterizations, coefficient estimates and differential subordination results for functions belonging to the class R?(?) are investigated. The Fekete-Szeg? coefficient functional associated with the kth root transform [f(zk)]1/k of functions in R?(?) is obtained. A similar problem for a corresponding class R?,?(?) of bi-univalent functions is also considered. Connections with previous known results are pointed out.

scholarly journals Coefficients of a Comprehensive Subclass of Meromorphic Bi-Univalent Functions Associated with the Faber Polynomial Expansion

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian
Keyword(s):  
Unit Disk ◽  
Univalent Functions ◽  
Expansion Method ◽  
Upper Bounds ◽  
Polynomial Expansion ◽  
Open Unit ◽  
Open Unit Disk ◽  
Faber Polynomial ◽  
The Subject ◽  
Polynomial Expansion Method

In this paper, we introduce a new comprehensive subclass ΣB(λ,μ,β) of meromorphic bi-univalent functions in the open unit disk U. We also find the upper bounds for the initial Taylor-Maclaurin coefficients |b0|, |b1| and |b2| for functions in this comprehensive subclass. Moreover, we obtain estimates for the general coefficients |bn|(n≧1) for functions in the subclass ΣB(λ,μ,β) by making use of the Faber polynomial expansion method. The results presented in this paper would generalize and improve several recent works on the subject.

scholarly journals The order of convexity for an integral operator

2016 ◽  
Vol 32 (1) ◽  
pp. 123-129
Author(s):  
VIRGIL PESCAR ◽  
◽  
CONSTANTIN LUCIAN ALDEA ◽  
◽  
Keyword(s):  
Integral Operator ◽  
Unit Disk ◽  
Analytic Functions ◽  
Univalent Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Order Of Convexity

In this paper we consider an integral operator for analytic functions in the open unit disk and we derive the order of convexity for this integral operator, on certain classes of univalent functions.

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 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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