A Note on Successive Coefficients of Convex Functions

Ming Li; Toshiyuki Sugawa

doi:10.1007/s40315-016-0177-8

A Note on Successive Coefficients of Convex Functions

Ming Li, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this note, we investigate the supremum and the infimum of the functional | a_n ₊ ₁| - | a_n| 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 | a_n ₊ ₁- a_n| for convex functions f with f^{′ ′}(0) = p for a prescribed p∈ [0 , 2].

Original language	English
Pages (from-to)	179-193
Number of pages	15
Journal	Computational Methods and Function Theory
Volume	17
Issue number	2
DOIs	https://doi.org/10.1007/s40315-016-0177-8
Publication status	Published - 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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AB - 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].

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KW - Successive coefficients

KW - Toeplitz determinant

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