Order Preserving Operator Function via Furuta Inequality “A ≥ B ≥ 0 Ensures for $$ \left( {A^{\frac{r} {2}} A^P A^{\frac{r} {2}} } \right)^{\frac{{1 + r}} {{p + r}}} \geqslant \left( {A^{\frac{r} {2}} B^p A^{\frac{r} {2}} } \right)^{\frac{{1 + r}} {{p + r}}} $$ for p≥1 and r≥0”

2000 ◽  
pp. 185-194
Author(s):  
Takayuki Furuta ◽  
Takeaki Yamazaki ◽  
Masahiro Yanagida
Keyword(s):  
Operator Function ◽  
Furuta Inequality

scholarly journals A decreasing operator function associated with the Furuta inequality

1998 ◽  
Vol 126 (8) ◽  
pp. 2427-2432 ◽  
Author(s):  
Takayuki Furuta ◽  
Derming Wang
Keyword(s):  
Operator Function ◽  
Furuta Inequality

scholarly journals Some Operator Inequalities on Chaotic Order and Monotonicity of Related Operator Function

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Changsen Yang ◽  
Yanmin Liu
Keyword(s):  
Operator Function ◽  
Type Operator ◽  
Operator Inequalities ◽  
Furuta Inequality ◽  
Related Operator

We will discuss some operator inequalities on chaotic order about several operators, which are generalization of Furuta inequality and show monotonicity of related Furuta type operator function.

Operator Function Method in the Problem of Normal Waves in an Inhomogeneous Waveguide

2018 ◽  
Vol 54 (9) ◽  
pp. 1168-1179 ◽  
Author(s):  
Yu. G. Smirnov ◽  
E. Yu. Smol’kin
Keyword(s):  
Function Method ◽  
Operator Function ◽  
Inhomogeneous Waveguide ◽  
Normal Waves

scholarly journals Furuta Inequality and its related topics

2010 ◽  
Vol 1 (2) ◽  
pp. 24-45 ◽  
Author(s):  
Masatoshi Fujii
Keyword(s):  
Furuta Inequality

scholarly journals Further extension of Furuta inequality

2010 ◽  
pp. 391-398
Author(s):  
Changsen Yang ◽  
Yaqing Wang
Keyword(s):  
Furuta Inequality

scholarly journals On the rate of convergence for a class of Markovian queues with group services

2020 ◽  
Vol 28 (3) ◽  
pp. 205-215
Author(s):  
Anastasia L. Kryukova
Keyword(s):  
Rate Of Convergence ◽  
Operator Function ◽  
Computer Network ◽  
Human Life ◽  
Queueing Models ◽  
Differential Inequalities ◽  
Queuing Systems ◽  
Stationary Model ◽  
Logarithmic Norm ◽  
Method Of Differential Inequalities

There are many queuing systems that accept single arrivals, accumulate them and service only as a group. Examples of such systems exist in various areas of human life, from traffic of transport to processing requests on a computer network. Therefore, our study is actual. In this paper some class of finite Markovian queueing models with single arrivals and group services are studied. We considered the forward Kolmogorov system for corresponding class of Markov chains. The method of obtaining bounds of convergence on the rate via the notion of the logarithmic norm of a linear operator function is not applicable here. This approach gives sharp bounds for the situation of essentially non-negative matrix of the corresponding system, but in our case it does not hold. Here we use the method of differential inequalities to obtaining bounds on the rate of convergence to the limiting characteristics for the class of finite Markovian queueing models. We obtain bounds on the rate of convergence and compute the limiting characteristics for a specific non-stationary model too. Note the results can be successfully applied for modeling complex biological systems with possible single births and deaths of a group of particles.

Sign in / Sign up

Export Citation Format

Share Document