Coefficient Estimates for a Subclass of Analytic Functions Associated with a Certain Leaf-Like Domain

Abstract

First, by making use of the concept of basic (or q-) calculus, as well as the principle of subordination between analytic functions, generalization Rq(h) of the class R(h) of analytic functions, which are associated with the leaf-like domain in the open unit disk U, is given. Then, the coefficient estimates, the Fekete–Szegö problem, and the second-order Hankel determinant H2(1) for functions belonging to this class Rq(h) are investigated. Furthermore, similar results are examined and presented for the functions zf(z) and f−1(z). For the validity of our results, relevant connections with those in earlier works are also pointed out.

Keywords

• analytic functions
• univalent functions
• bounded turning functions
• <i>q</i>-derivative (or <i>q</i>-difference) operator
• principle of subordination between analytic functions
• leaf-like domain