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In this paper our aim is to study some valuable problems dealing with newly defined subclass of multivalent q -starlike functions. These problems include the initial coefficient estimates, Toeplitz matrices, Hankel determinant, Fekete-Szego problem, upper bounds of the functional a+₁- a+₁^2 for the subclass of multivalent q -starlike functions. As applications we study a q -Bernardi integral operator for a subclass of multivalent q -starlike functions. Furthermore, we also highlight some known consequence of our main results.
Tang et al. (Fri,) studied this question.