Some Extensions of Coecient Problems for Bi-Univalent Ma-Minda Starlike and Convex Functions

Liangpeng Xiong, Xiaoli Liu


Motivated by the works of H.M.Srivastava et al. [7], we introduce
and investigate two new general subclasses $\mathcal {H}_\mathcal
{T}(\varphi,\psi,\alpha)$,$\mathcal {H}^{h,p}_\mathcal {T}(\alpha)$
of bi-starlike and bi-convex of Ma-Minda type functions. Bounds on
the first two coefficients $|a_2|$ and $|a_3|$ for functions in
$\mathcal {H}_\mathcal {T}(\varphi,\psi,\alpha)$ and $\mathcal
{H}^{h,p}_\mathcal {T}(\alpha)$ are given. The results here
generalize and improve the corresponding earlier works done by Ali
et al.[1] and Brannan et al.[2].

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