Barbour path functions and related operator means

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1 Citation (Scopus)


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
Issue number8
Publication statusPublished - Oct 15 2013
Externally publishedYes


  • Operator mean
  • Operator monotone function
  • Path

ASJC Scopus subject areas

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


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