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.
In the present investigation we introduce some subclasses of the function class Σ of bi-univalent functions defined in the open unit disk U, which are associated with the quasi-subordination. We obtain the estimates on initial coefficients |a 2 | and |a 3 | for the functions in these subclasses. Also several related subclasses are considered and connection with some known results are established.
Abstract:In recent years, the study of bi-univalent functions have gathered momentum mainly due to the pioneering work of Srivastava et al. [19], which has actually revived the study of the coefficient problems involving bi-univalent functions. With motivation from the work of Srivastava et al. [19], in the present paper we introduce a new subclass T Σ [φ ] of the function class Σ of bi-univalent functions defined in the open unit disk U = {z ∈ C : |z| < 1}. Further, for the functions in this subclass T Σ [φ ] we obtain bounds on |a 2 |, |a 3 | and |a 4 |.
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.
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