A Note on Successive Coefficients of Convex Functions

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8 Citations (Scopus)

Abstract

In this note, we investigate the supremum and the infimum of the functional | an + 1| - | an| for functions, convex and analytic on the unit disk, of the form f(z) = z+ a2z2+ a3z3+ ⋯. We also consider the related problem of maximizing the functional | an + 1- an| for convex functions f with f′ ′(0) = p for a prescribed p∈ [0 , 2].

Original languageEnglish
Pages (from-to)179-193
Number of pages15
JournalComputational Methods and Function Theory
Volume17
Issue number2
DOIs
Publication statusPublished - 2017 Jun 1

Keywords

  • Convex function
  • Successive coefficients
  • Toeplitz determinant

ASJC Scopus subject areas

  • Analysis
  • Computational Theory and Mathematics
  • Applied Mathematics

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