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In this work, we investigate the (p, q)-Gegenbauer polynomials for a class of analytic and bi-univalent functions defined in the open unit disk, with respect to subordination. We give an elementary proof to establish some estimates for the coefficient bounds for functions in the new class. We conclude the study by giving a result of the Fekete-Szegö theorem. A corollary was given to show some results of some subclasses of our new class.
Oyekan et al. (Mon,) studied this question.