scholarly journals Some Properties of Furuta Type Inequalities and Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Jiangtao Yuan ◽  
Caihong Wang
Keyword(s):  
Operator Equation ◽  
Type Operator ◽  
Heinz Inequality ◽  
Furuta Inequality

This work is to consider Furuta type inequalities and their applications. Firstly, some Furuta type inequalities underA≥B≥0are obtained via Loewner-Heinz inequality; as an application, a proof of Furuta inequality is given without using the invertibility of operators. Secondly, we show a unified satellite theorem of grand Furuta inequality which is an extension of the results by Fujii et al. At the end, a kind of Riccati type operator equation is discussed via Furuta type inequalities.

scholarly journals The additive approximation on a four-variate Jensen-type operator equation

2003 ◽  
Vol 2003 (50) ◽  
pp. 3171-3187 ◽  
Author(s):  
Jian Wang
Keyword(s):  
Functional Equation ◽  
Operator Equation ◽  
Stability Theory ◽  
Close Relation ◽  
Type Operator ◽  
Ulam Stability ◽  
Additive Approximation ◽  
Error Formulas ◽  
Rassias Stability

We study the Hyers-Ulam stability theory of a four-variate Jensen-type functional equation by considering the approximate remainderϕand obtain the corresponding error formulas. We bring to light the close relation between theβ-homogeneity of the norm onF∗-spaces and the approximate remainderϕ, where we allowp,q,r, andsto be different in their Hyers-Ulam-Rassias stability.

Integrable solutions of a mixed type operator equation

2010 ◽  
Vol 216 (4) ◽  
pp. 1150-1157 ◽  
Author(s):  
M.A. Taoudi ◽  
N. Salhi ◽  
B. Ghribi
Keyword(s):  
Operator Equation ◽  
Mixed Type ◽  
Type Operator

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.

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