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 language | English |
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Pages (from-to) | 2434-2441 |
Number of pages | 8 |
Journal | Linear Algebra and Its Applications |
Volume | 439 |
Issue number | 8 |
DOIs | |
Publication status | Published - Oct 15 2013 |
Externally published | Yes |
Keywords
- Operator mean
- Operator monotone function
- Path
ASJC Scopus subject areas
- Algebra and Number Theory
- Numerical Analysis
- Geometry and Topology
- Discrete Mathematics and Combinatorics