Sharp bounds for the initial coefficients for certain families of bi-univalent functions
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In our study, we present the well known family ${\mathcal N}_\Sigma^\mu(\lambda)$ of $\Sigma$, which is the family of bi-univalent functions in the open unit disk ${\mathbb U}$. We obtain sharp estimates for the first three Taylor-Maclaurin coefficients $|a_2|$, $|a_3|$, $|a_4|$. Fekete-Szeg\"{o} functional problem is also established. Furthermore, we consider the family ${\mathcal B}_{1,\Sigma}(\mu,\lambda,\gamma)$ of bi-univalent functions in the open unit disk ${\mathbb U}$. The results presented in this paper would generalize and improve some recent works of several earlier authors.
Abstract
In our study, we present the well known family ${\mathcal N}_\Sigma^\mu(\lambda)$ of $\Sigma$, which is the family of bi-univalent functions in the open unit disk ${\mathbb U}$. We obtain sharp estimates for the first three Taylor-Maclaurin coefficients $|a_2|$, $|a_3|$, $|a_4|$. Fekete-Szeg\"{o} functional problem is also established. Furthermore, we consider the family ${\mathcal B}_{1,\Sigma}(\mu,\lambda,\gamma)$ of bi-univalent functions in the open unit disk ${\mathbb U}$. The results presented in this paper would generalize and improve some recent works of several earlier authors.
참고문헌 (18)
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