Abstract

In this present paper, we introduce two new subclasses $\mathcal{H}^{k}_{\Sigma}(\alpha, \delta, \lambda,\mu,\sigma)$ and $\mathcal{H}^{k}_{\Sigma}(\beta, \delta, \lambda,\mu,\sigma)$ of normalized analytic bi-univalent functions defined in the open unit disk and associated with generalized differential operator. Further, we obtain bounds for the second and third Taylor- Maclaurin coefficients of the functions of these subclasses. Also, we obtain some consequences of results obtained.

Keywords and Phrases

Analytic function, Univalent function, Bi-Univalent function, Taylor-Maclaurin series.

A.M.S. subject classification

30C45.

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