kantorovich constant
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2021 ◽  
Vol 73 (1) ◽  
pp. 23-32
Author(s):  
A. Beiranvand ◽  
A. G. Ghazanfari

UDC 517.9 We present numerous refinements of the Young inequality by the Kantorovich constant. We use these improved inequalities to establish corresponding operator inequalities on a Hilbert space and some new inequalities involving the Hilbert –  Schmidt norm of matrices.  



2020 ◽  
Vol 72 (10) ◽  
pp. 1443-1451
Author(s):  
Z. Heydarbeygi ◽  
M. Amyari ◽  
M. Khanehgir

UDC 517.5 In this paper, we give some refinements for the second inequality in   where   In particular, if is hyponormal by refining the Young inequality with the Kantorovich constant   we show that   where and . We also give a reverse for the classical numerical radius power inequality  for any operator in the case when  



2020 ◽  
Vol 70 (2) ◽  
pp. 453-466
Author(s):  
A. Beiranvand ◽  
Amir Ghasem Ghazanfari

Abstract In this paper, we present numerous refinements of the Young inequality by the Kantorovich constant. We use these improved inequalities to establish corresponding operator inequalities on a Hilbert space and some new inequalities involving the Hilbert-Schmidt norm of matrices. We also give some refinements of the following Heron type inequality for unitarily invariant norm |||⋅||| and A, B, X ∈ Mn(ℂ): $$\begin{array}{} \begin{split} \displaystyle \Big|\Big|\Big|\frac{A^\nu XB^{1-\nu}+A^{1-\nu}XB^\nu}{2}\Big|\Big|\Big| \leq &(4r_0-1)|||A^{\frac{1}{2}}XB^{\frac{1}{2}}||| \\ &+2(1-2r_0)\Big|\Big|\Big|(1-\alpha)A^{\frac{1}{2}}XB^{\frac{1}{2}} +\alpha\Big(\frac{AX+XB}{2}\Big)\Big|\Big|\Big|, \end{split} \end{array}$$ where $\begin{array}{} \displaystyle \frac{1}{4}\leq \nu \leq \frac{3}{4}, \alpha \in [\frac{1}{2},\infty ) \end{array}$ and r0 = min{ν, 1 – ν}.



2020 ◽  
Vol 27 (1) ◽  
pp. 38-51
Author(s):  
F. M. Dannan


Filomat ◽  
2020 ◽  
Vol 34 (11) ◽  
pp. 3639-3654
Author(s):  
Changsen Yang ◽  
Yu Li

In this paper, we gave a new Young type inequality and the relevant Heinz mean inequality. Furthermore, we also improved some inequalities with Kantorovich constant or Specht?s ratio. Meanwhile, on the base of our scalars results, we obtain some new corresponding operator inequalities and matrix versions including Hilbert-Schmidt norm, unitarily invariant norm and related trace versions, which can be regarded as the application of our scalar results.



2018 ◽  
Vol 74 (1) ◽  
Author(s):  
Leila Nasiri ◽  
Mahmood Shakoori
Keyword(s):  


2018 ◽  
Vol 55 (3) ◽  
pp. 363-373
Author(s):  
Leila Nasiri ◽  
Andrei A. Shkalikov ◽  
Mahmood Shakoori

In present paper, we give some new reverses of the Young type inequalities which were established by X. Hu and J. Xue [7] via Kantorovich constant. Then we apply these inequalities to establish corresponding inequalities for the Hilbert-Schmidt norm and the trace norm.



2018 ◽  
Vol 68 (4) ◽  
pp. 803-810
Author(s):  
Maryam Khosravi

Abstract The main objective of the present paper, is to obtain some new versions of Young-type inequalities with respect to two weighted arithmetic and geometric means and their reverses, using two inequalities $$\begin{array}{} \displaystyle K\Big(\frac{b}{a},2\Big)^r\leq\frac{a\nabla_{\nu}b}{a\sharp_{\nu}b}\leq K\Big(\frac{b}{a},2\Big)^R, \end{array}$$ where r = min{ν, 1 – ν}, R = max{ν,1 – ν} and K(t,2) = $\begin{array}{} \displaystyle \frac{(t+1)^2}{4t} \end{array}$ is the Kantorovich constant, and $$\begin{array}{} \displaystyle e(h^{-1},\nu)\leq\frac{a\nabla_{\nu}b}{a\sharp_{\nu}b}\leq e(h,\nu), \end{array}$$ where h = max $\begin{array}{} \displaystyle \{\frac{a}{b},\frac{b}{a}\} \end{array}$ and e(t,ν) = exp (4ν(1 – ν)(K(t,2)–1) $\begin{array}{} \displaystyle (1-\frac{1}{2t})\big). \end{array}$ Also some operator versions of these inequalities and some inequalities related to Heinz mean are proved.



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