Application of Gegenbauer polynomials for biunivalent functions defined by subordination

Authors: FETHİYE MÜGE SAKAR, SAQIB HUSSAIN, IBRAR AHMAD

Abstract: We present and investigate a new subclass of biunivalent functions by applying Gegenbouer polynomials in this paper. Also, we find nonsharp estimates on the first two coefficients $\left \vert b_{0}\right \vert$ and $% \left \vert b_{1}\right \vert$ for functions belonging to this subclass. Furthermore, the Fekete-Szegö inequality $\left \vert b_{1}-\eta b_{0}^{2}\right \vert$ for this subclass is obtained. We also point out some consequences of results.

Keywords: Gegenbauer polynomials, coefficient estimates, biunivalent functions and subordination

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