The Fekete-Szego theorem for close-to-convex functions of the class K sh(α, β)

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6 Citations (Scopus)

Abstract

For 0 ≤ α < 1 and 0 < β ≤ 1. Let K sh(α, β) be the class of normalized close-to-convex functions defined in the open unit disc D by |arg(zf′(z)/g(z))| ≤ πα/2, such that g ∈ S* (β), the class of analytic normalized starlike functions of order β, i.e. for z ∈ D, ℜ(zg′(z)/g(z)) > β. For f ∈ Ksh(α, β) and given by f(z) = z + a2z2 + a3z 3 + ⋯ , some sharp bounds are obtained for the Fekete-Szego functional |a3 - μa2 2| when μ is real.

Original languageEnglish
Pages (from-to)13-18
Number of pages6
JournalActa Mathematica Academiae Paedagogicae Nyiregyhaziensis
Volume18
Issue number1
Publication statusPublished - 2002

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Close-to-convex Functions
Sharp Bound
Theorem
Class

Keywords

  • Close-to-convex functions
  • Convex
  • Fekete-Szego theorem
  • Starlike

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

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