scholarly journals Coefficient bounds for a certain class of analytic and bi-univalent functions

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.

Axioms ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 27
Author(s):  
Hari Mohan Srivastava ◽  
Ahmad Motamednezhad ◽  
Safa Salehian

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.


Author(s):  
Ismaila O. Ibrahim ◽  
Timilehin G. Shaba ◽  
Amol B. Patil

In the present investigation, we introduce the subclasses $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\phi,\upsilon)$ and $\Lambda_{\Sigma_m}^{\rightthreetimes}(\sigma,\gamma,\upsilon)$ of $m$-fold symmetric bi-univalent function class $\Sigma_m$, which are associated with the Sakaguchi type of functions and defined in the open unit disk. Further, we obtain estimates on the initial coefficients $b_{m+1}$ and $b_{2m+1}$ for the functions of these subclasses and find out connections with some of the familiar classes.


Author(s):  
Timilehin G. Shaba ◽  
Amol B. Patil

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.


Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1305-1313
Author(s):  
Amol Patil ◽  
Uday Naik

In the present investigation, with motivation from the pioneering work of Srivastava et al. [28], which in recent years actually revived the study of analytic and bi-univalent functions, we introduce the subclasses T*?(n,?) and T?(n,?) of analytic and bi-univalent function class ? defined in the open unit disk U = {z ? C : |z| < 1g and involving the S?l?gean derivative operator Dn. Moreover, we derive estimates on the initial coefficients |a2| and |a3| for functions in these subclasses and pointed out connections with some earlier known results.


Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1313-1322 ◽  
Author(s):  
H.M. Srivastava ◽  
Müge Sakar ◽  
Güney Özlem

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.


2018 ◽  
Vol 68 (2) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmad Zireh ◽  
Ebrahim Analouei Adegani ◽  
Mahmood Bidkham

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.


2021 ◽  
Vol 20 ◽  
pp. 105-114
Author(s):  
Najah Ali Jiben Al-Ziadi

\In this work we present and investigate three new subclasses of  the function class  of bi-univalent functions in the open unit disk  defined by means of the Horadam polynomials. Furthermore, for functions in each of the subclasses introduced here, we obtain upper bounds for the initial coefficients  and . Also, we debate Fekete-Szegӧ inequality for functions belongs to these subclasses.    


2021 ◽  
Vol 26 (2) ◽  
pp. 52-65
Author(s):  
Najah Ali Jiben Al-Ziadi ◽  
Abbas Kareem Wanas

In the present paper, by making use the Horadam polynomials, we introduce and investigate two new subclasses  and  of the function class  of holomorphic bi-univalent functions in the open unit disk Δ. For functions belonging to this subclasses, we obtain upper bounds for the second and third coefficients and discuss Fekete-Szegӧ problem. Furthermore, we point out several new special cases of our results.


2021 ◽  
Vol 20 ◽  
pp. 630-636
Author(s):  
S. R. Swamy ◽  
Alina Alb Lupaş ◽  
Abbas Kareem Wanas ◽  
J. Nirmala

In this paper, by making use of Borel distribution we introduce a new family GΣ(δ, γ, λ, τ, r) of normalized analytic and bi-univalent functions in the open unit disk U, which are associated with Horadam polynomials. We establish upper bounds for the initial Taylor-Maclaurin coefficients |a2| and |a3| of functions belonging to the analytic and bi-univalent function family which we have introduced here. Furthermore, we establish the Fekete-Szego problem of functions in this new family.


2019 ◽  
Vol 12 (02) ◽  
pp. 1950017
Author(s):  
H. Orhan ◽  
N. Magesh ◽  
V. K. Balaji

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass [Formula: see text] of analytic bi-univalent function class [Formula: see text] which is associated with Chebyshev polynomials in the open unit disk.


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