Coefficient bounds and convolution properties for certain classes of close-to-convex functions

Yong Chan Kim, Jae Ho Choi, Toshiyuki Sugawa

Research output: Contribution to journalArticlepeer-review

27 Citations (Scopus)


A number of authors (cf. Koepf [4], Ma and Minda [6]) 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.

Original languageEnglish
Pages (from-to)95-98
Number of pages4
JournalProceedings of the Japan Academy Series A: Mathematical Sciences
Issue number6
Publication statusPublished - 2000
Externally publishedYes


  • Coefficient bound
  • Convolution
  • Univalent function

ASJC Scopus subject areas

  • Mathematics(all)


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