Initial Coefficients Estimate and Fekete-Szegö Problems for Two New Subclasses of Bi-Univalent Functions

Abstract

In the present investigation, making use of definition of the generalized Bivariate Fibonacci-Like polynomials that include polynomials such as Horadam, Chebyshev polynomials two new subclasses of bi-univalent functions are introduced. Then, some bounds are determined for the initial Taylor-Maclaurin coefficients of the functions belonging to these new subclasses. Further, the well-known Fekete-Szegö problem is discussed for the defined subclasses. Lastly, several remarks are indicated for the some special values of variables.

Keywords

• Bi-univalent function
• bivariate Fibonacci polynomials
• coefficient estimates
• Fekete-Szeg\"{o} functional
• Horadam polynomials

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