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Keywords:
analytic function; bi-univalent function; subordination; Fekete-Szegö functional; Gegenbauer polynomial
analytic function; bi-univalent function; subordination; Fekete-Szegö functional; Gegenbauer polynomial
Summary:
In the present article, the authors introduce two new subclasses of holomorphic and bi-univalent functions with respect to the symmetric points defined in the domain of open unit disk $\Delta :=\{z \in \mathbb {C}\colon |z|<1\}$ by making use of subordination between two analytic functions and also using the Gegenbauer polynomials. We investigate bounds of some of the initial Taylor-Maclaurin coefficients belonging to this newly constructed holomorphic and bi-univalent function class. Moreover, we derive the well-known Fekete-Szegö functional for the above said classes. Some of the corollaries of the main results are pointed out.
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