• 대한수학회논문집
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• 제32권2호
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• pp.389-397
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• 2017

In this paper, we introduce and investigate an interesting subclass of meromorphic bi-univalent functions defined on ${\Delta}=\{z{\in}{\mathbb{C}}$ : 1 < |z| < ${\infty}\}$. For functions belonging to this class, estimates on the initial coefficients are obtained. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Kyungpook Mathematical Journal
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• 제58권4호
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• pp.697-709
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• 2018

In the present paper, we introduce and investigate two new subclasses, namely; the class of strongly ${\alpha}$-bi-spirallike functions of order ${\beta}$ and ${\alpha}$-bi-spirallike functions of order ${\rho}$, of the function class ${\Sigma};$ of normalized analytic and bi-univalent functions in the open unit disk $$U=\{z:z{\in}C\;and\;{\mid}z{\mid}<1\}$$. We find estimates on the coefficients ${\mid}a_2{\mid}$, ${\mid}a_3{\mid}$ and ${\mid}a_4{\mid}$ for functions in these two subclasses.

• 호남수학학술지
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• 제40권4호
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• pp.733-748
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• 2018

In this paper, we investigate a new subclass $S^{{\varphi},{\lambda}}_{{\Sigma}_m}$ of ${\Sigma}_m$ consisting of analytic and m-fold symmetric bi-univalent functions satisfying subordination in the open unit disk U. We consider the Fekete-$Szeg{\ddot{o}}$ inequalities for this class. Also, we establish estimates for the coefficients for this subclass and several related classes are also considered and connections to earlier known results are made.

• 호남수학학술지
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• 제41권2호
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• pp.381-390
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• 2019

In this paper, we introduce interesting subclasses ${\mathcal{H}}^{p,q,{\beta},{\alpha}}_{{\sigma}B}$ and ${\mathcal{H}}^{p,q,{\beta}}_{{\sigma}B}({\gamma})$ of bi-univalent functions by (p, q)-derivative operator. Furthermore, we find upper bounds for the second and third coefficients for functions in these subclasses. The results presented in this paper would generalize and improve some recent works of several earlier authors.

• Korean Journal of Mathematics
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• 제30권1호
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• pp.73-80
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• 2022

In this article, we represent and examine a new subclass of holomorphic and bi-univalent functions defined in the open unit disk 𝖀, which is associated with the Dziok-Srivastava operator. Additionally, we get upper bound estimates on the Taylor-Maclaurin coefficients |a₂| and |a₃| of functions in the new class and improve some recent studies.

• 호남수학학술지
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• 제42권2호
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• pp.319-330
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• 2020

We introduce a new subclass of q-bi-univalent functions of complex order related to shell-like curves connected with the Fibonacci numbers. We obtain the coefficient estimates and Fekete-Szegö inequalities for the functions belonging to this class. Relevant connections with various other known classes have been illustrated.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.647-657
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• 2023

The aim of this paper is to study certain subclass ${\tilde{S^q_{\Sigma}}}({\lambda},\,{\alpha},\,t,\,s,\,p,\,b)$ of analytic and bi-univalent functions which are defined by using symmetric q-derivative operator. We estimate the second and third coefficients of the Taylor-Maclaurin series expansions belonging to the subclass and upper bounds for Feketo-Szegö inequality. Furthermore, some relevant connections of certain special cases of the main results with those in several earlier works are also pointed out.

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.493-503
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• 2019

In the present investigation, we define two new subclasses of analytic and m-fold symmetric bi-univalent functions defined by a linear combination in the open unit disk U. Furthermore, for functions in each of the subclasses introduced here, we establish upper bounds for the initial coefficients ${\mid}a_{m+1}{\mid}$ and ${\mid}a_{2m+1}{\mid}$. Also, we indicate certain special cases for our results.

• Kyungpook Mathematical Journal
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• 제55권3호
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• pp.705-714
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• 2015

In this paper, we introduce and investigate an interesting subclass $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ of analytic and bi-univalent functions of complex order in the open unit disk ${\mathbb{U}}$. For functions belonging to the class $M_{\Sigma}({\gamma},{\lambda},{\delta},{\varphi})$ we investigate the coefficient estimates on the first two Taylor-Maclaurin coefficients ${\mid}{\alpha}_2{\mid}$ and ${\mid}{\alpha}_3{\mid}$. The results presented in this paper would generalize and improve some recent works of [1],[5],[9].

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.341-350
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• 2022

We introduce certain subclasses of bi-univalent functions related to the strongly Janowski functions and discuss the Taylor-Maclaurin coefficients |a₂| and |a₃| for the newly defined classes. Also, we deduce certain new results and known results as special cases of our investigation.