Barbour path functions and related operator means

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

We consider Barbour path function Fx(a,b)=a×bax+ba(1-x) x+ba(1-x) (0≤x≤1, a,b>0) as an approximation of the exponential function (or the geometric mean path) Gx(a,b)=a1-x bx (0≤x≤1, a,b>0) by a linear fractional function, which interpolates Gx(a,b) at x=0,12 and 1. If a=1 and b=t, then both the functions Fx(1,t) and Gx(1,t) are operator monotone in t, parameterized with x. We also consider the order relation between the integral mean for the Barbour path function and another mean.

Original languageEnglish
Pages (from-to)2434-2441
Number of pages8
JournalLinear Algebra and Its Applications
Volume439
Issue number8
DOIs
Publication statusPublished - Oct 15 2013
Externally publishedYes

Fingerprint

Operator Mean
Mathematical operators
Path
Integral Means
Order Relation
Geometric mean
Monotone Operator
Exponential functions
Fractional
Interpolate
Approximation

Keywords

  • Operator mean
  • Operator monotone function
  • Path

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology
  • Numerical Analysis

Cite this

Barbour path functions and related operator means. / Nakamura, Noboru.

In: Linear Algebra and Its Applications, Vol. 439, No. 8, 15.10.2013, p. 2434-2441.

Research output: Contribution to journalArticle

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