Upper bound of the third Hankel determinant for a subclass of q-starlike functions associated with the q-exponential function

Abstract

By making use of the concept of basic (or q-) calculus, a subclass S⁎(L,q) of q-starlike functions, which is associated with the q-exponential function, is introduced here in the open unit disk U given byU={z:z∈Cand|z|<1}. The main object of this article is to determine the upper bound of the third-order Hankel determinant H3(1) for functions belonging to the q-starlike function class S⁎(L,q). For validity of our results, relevant connections with those in earlier works are also pointed out.