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

#### Abstract

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].

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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