A number of authors (cf. Koepf , Ma and Minda ) have been studying the sharp upper bound on the coefficient functional |a3- μa22| for certain classes of univalent functions. In this paper, we consider the class C(φ, ψ) of normalized close-to-convex functions which is defined by using subordination for analytic functions φ and ψ on the unit disk. Our main object is to provide bounds of the quantity a3 - μa22 for functions f(z) = z + a2Z2 + a3z3 + ⋯ in C(φ, ψ) in terms of φ and ψ, where μ is a real constant. We also show that the class C(φ, ψ) is closed under the convolution operation by convex functions, or starlike functions of order 1/2 when φ and ψ satisfy some mild conditions.
|Number of pages||4|
|Journal||Proceedings of the Japan Academy Series A: Mathematical Sciences|
|Publication status||Published - 2000|
- Coefficient bound
- Univalent function