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

Year 2022, Volume: 10 Issue: 1, 138 - 148, 15.04.2022

İbrahim Aktaş , Nazmiye Yılmaz

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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