Abstract

In the present work, we investigate a new subclass of bi-univalent functions by applying the $q$-derivative operator associated with Chebyshev polynomials. We find estimates for the general Taylor-Maclaurin coefficients of the functions in this class and also obtain an estimation for the Fekete-Szeg$\ddot{o}$ problem for this class.

Keywords and Phrases

Analytic functions, Univalent and Bi-univalent functions, Fekete-Szeg$\ddot{o}$ inequality, Chebyshev polynomials and $q$-derivative operator.

A.M.S. subject classification

Primary 30C45, Secondary 30C50.

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