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 |
|---|---|
| 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 |
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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 journal › Article
}
TY - JOUR
T1 - Barbour path functions and related operator means
AU - Nakamura, Noboru
PY - 2013/10/15
Y1 - 2013/10/15
N2 - 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.
AB - 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.
KW - Operator mean
KW - Operator monotone function
KW - Path
UR - http://www.scopus.com/inward/record.url?scp=84882876729&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84882876729&partnerID=8YFLogxK
U2 - 10.1016/j.laa.2013.06.035
DO - 10.1016/j.laa.2013.06.035
M3 - Article
AN - SCOPUS:84882876729
VL - 439
SP - 2434
EP - 2441
JO - Linear Algebra and Its Applications
JF - Linear Algebra and Its Applications
SN - 0024-3795
IS - 8
ER -