Coefficient Estimates for the Generalized Subclass of Analytic and Bi-univalent Functions

Authors

  • Haigen Xiao
  • Qing Hua Xu

Keywords:

Analytic functions, Univalent functions, Bi-univalent functions, Coefficient bounds and coefficient estimates

Abstract

In this paper, we introduce and investigate an interesting subclass $\mathcal{B}_\Sigma^{h,p}(\lambda)$ of analytic and bi-univalent functions in the open unit disk $\mathbb{U}$. For functions belonging to the class $\mathcal{B}_\Sigma^{h,p}(\lambda)$, obtain estimates on the first two coefficients $|a_2|$ and $|a_3|$. The results presented in this paper generalize and improve some recent works of Frasin et al. [B.A.Frasin, M.K.Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett. 24(2011) 1569-1573] and Srivastava et al. [Qing-Hua Xu, Ying-Chun Gui, H.M.Srivastava, coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. Appl. Math. Lett. 25: 990-994, 2012].

Author Biography

Qing Hua Xu

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How to Cite

Xiao, H., & Xu, Q. H. (2017). Coefficient Estimates for the Generalized Subclass of Analytic and Bi-univalent Functions. European Journal of Pure and Applied Mathematics, 10(4), 638–644. Retrieved from https://ejpam.com/index.php/ejpam/article/view/2546