Applications of the Horadam polynomials involving λ-pseudo-starlike bi-univalent functions associated with a certain convolution operator

In this article, we introduce and study a new family P?(?,?,k,?,?,?,r) of normalized analytic ?-pseudo-starlike bi-univalent functions by using the Horadam polynomials, which is associated with certain convolution operator defined in open unit disk U. We establish bounds for |a2| |a3|, where a2, a3 are initial Taylor-Maclaurin coefficients. Furthermore, obtain Fekete-Szeg? inequality class P? (?,?,k,?,?,?,r), have introduced here. indicate several special cases consequences our results. Finally, comment on recent usages, especially Geometric Function Theory Complex Analysis, basic (or q-) calculus also its trivial inconsequentional (p,q)-variation involving an obviously redundant parameter p.